This almost works but it includes my first record

Notwithstanding 1nickt's excellent advice (which you should heed) there's a trivial adjustment to your script which should do what you want. Just read and print the first line before you sort the rest.

print $fDest <$fSource>;
[download]

Untested* but simple enough that hopefully the gist is obvious. BTW, it will help your cause for future posts if you wrap your code in <code> ... </code> tags as I have done here.

*Update: As AnomalousMonk has pointed out below (++) you'll need to enforce scalar context here.

print $fDest <$fSource>;

Reading from  <> (see readline) in the list context imposed by the argument list of print will read all lines from the filehandle. For reading just one line, use something like:
    print $fDest scalar <$fSource>;
to impose scalar context (see scalar).

---

Give a man a fish:  <%-{-{-{-<

use DBI;
use 5.014;
use warnings;

# See "Creating database handle" below
my $dbh = DBI->connect ("dbi:CSV:", undef, undef, {
    f_ext      => ".csv/r",
    RaiseError => 1,
    }) or die "Cannot connect: $DBI::errstr";
my $sth=$dbh->prepare("select * from data order by SUPPLIER_CODE;");
$sth->execute();
local $"=q{,};
while (my $values_aref=$sth->fetchrow_arrayref ) {
    #warn Data::Dumper->Dump([\$values_aref],[qw(*values)]),' ';
    print "@$values_aref\n";
    };
[download]

THIS. If you have data, treat it as data. It's a bit more work to set up the first time, but after that it's so much easier - switching from csv to sqlite to mysql to Db2 to ... doesn't matter, it's so much easier once you see your data as actual data rather than a file format to fight with.

Life has taken me far afield from Perl (mostly C# and Javascript nowadays), but there's so much I've learned in perl that is relatively straight forward in other languages. Except this one: treating a csv file as a source for SQL without having to import it into an actual database system. There's lots I miss about perl, and many things in other languages that are the same (with a different, usually longer, syntax), but this one tops my list. You're using perl, take advantage of it.

I agree.

However, there is a another step in-between text and database, in the form of a "Foreign Data Wrapper", to let the database serve up the underlying (csv-)textfile:

psql -qX << SQL_TXT
create server if not exists temp_fs foreign data wrapper file_fdw;
drop   foreign table if exists ft_pm2 cascade;
create foreign table           ft_pm2 (
    "CAT_HEADER" text
  , "SUPPLIER_CODE" text
  , "CUSTOMER_CODE" text
  , "F4" text
  , "F5" text
  , "F6" text
  , "F7" text
  , "F8" numeric
)
server temp_fs
options (
     format 'csv'
   , header 'true'
   , filename '/tmp/data.txt'
);
copy(select * from ft_pm2 order by 2, 3) to stdout with (format csv, h
+eader true);
SQL_TXT
[download]

Results are (again):

CAT_HEADER,SUPPLIER_CODE,CUSTOMER_CODE,F4,F5,F6,F7,F8
CAT_LINE,0001P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0001P,ABC23456,20190924,,1,Z,2.14
CAT_LINE,0001P,ABC34567,20190924,,1,Z,12.23
CAT_LINE,0002P,ABC12345,20190924,,1,Z,4.26
CAT_LINE,0002P,ABC23456,20190924,,1,Z,1.21
CAT_LINE,0002P,ABC34567,20190924,,1,Z,22.24
[download]

Such SQL using a 'Foreign Table' reads the underlying csv/text file(s). The annoying part is setting up the table , for instance in the case of tables with hundreds of columns you need a separate little application to do that, and this is where perl comes in handy (reading the header line and turning it into the CREATE TABLE column-list).

Weaknesses and strengths:

Advantages: SQL access to csv data. DBD::CSV delivers SQL as in SQL::Statement::Syntax which is nice but basic. The Data Wrapper's Foreign Table gives you access to the data via the full postgres SQL engine: Window Functions, Grouping Sets/Cube/Rollup, Generated Columns, Partitioning , etc., etc.)

Disadvantages: Needs Postgres, and with extension file_fdw installed. Table remains read-only. No indexing possible, so that huge csv-files can make it slow (alhough 'copying' onto a materialized view [3] on the foreign table makes of course indexing possible again). Filesystem access for the postgres superuser is necessary.

It all depends what you want to do.

[1] file_fdw - this foreign data wrapper reads text files

[2] Create Server

[3] Create Foreign Table

[4] Create Materialized View

Hi welcome to Perl, the One True Religion.

Use the right tools.

• Text::CSV for CSV/TSV files
• Path::Tiny for general file handling

Sure, you can do it with split. You can hang yourself if you have enough rope, which Perl will happily give you. Other forebears have made a simple, safe and powerful tool for most standard tasks. Do not buy the lie that it's too much work or too difficult or not permitted or not needed or not performant enough to go to the CPAN and use the right tool for the job.

Use the right tool, and dedicate your time to solving your own program/logic flow.

Hope this helps!

There are utilities available outside of Perl that can do what the OP is asking about: *nix sort (which can do multi-field/multi-key sorting and may be able to handle very large files), head, tail and cat. These are also available as "Unix utilities for Windows", which is what I'm using, but you'll have to Google for an appropriate package of these binaries. Here's a Windows command-line session using your OPed example .csv file (BTW: Code tags should be used for input/output and data as well as code):

#!/usr/bin/perl

use strict;
use warnings;

my $file = shift or die;      # read csv file...
my $hash;

open my $fh, "<", $file;
my $result = <$fh>;           # grab header...
while ( my $line = <$fh> ) {  # then read rest of file.
  push @{$hash->{ [ split /,/, $line ]->[1] }}, $line;
}

$result .= join '', @{$hash->{$_}}
  for sort keys $hash;

print $result;

__output__
CAT_HEADER,SUPPLIER_CODE,CUSTOMER_CODE
CAT_LINE,0001P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0001P,ABC23456,20190924,,1,Z,2.24
CAT_LINE,0001P,ABC34567,20190924,,1,Z,2.24
CAT_LINE,0002P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0002P,ABC23456,20190924,,1,Z,2.24
CAT_LINE,0002P,ABC34567,20190924,,1,Z,2.24
[download]

Admittedly just for my own fun I did it via a database (postgres 12.0). Don't do this at home --- although it isn't actually too bad, and only /just/ a bit more than a one-liner... I added the missing column names as I assume they are normally there in the real data.

#!/bin/bash

echo "CAT_HEADER,SUPPLIER_CODE,CUSTOMER_CODE,F4,F5,F6,F7,F8
CAT_LINE,0001P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0002P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0001P,ABC23456,20190924,,1,Z,2.24
CAT_LINE,0002P,ABC23456,20190924,,1,Z,2.24
CAT_LINE,0001P,ABC34567,20190924,,1,Z,2.24
CAT_LINE,0002P,ABC34567,20190924,,1,Z,2.24" > data.txt

head -n 1 data.txt | perl -ne 'chomp; print "
drop table if exists pm11107044 ;
create table pm11107044 (" . join(",", map {"\"$_\" text"} split(/,/, 
+$_)) . ");";
' | psql -qX && < data.txt psql -qXc "copy pm11107044 from stdin with 
+(format csv, header true);"

echo "-- unordered data.txt:"
cat data.txt
echo

echo "-- ordered data:"
echo "select * from pm11107044 order by 2, 3" | psql -qX --csv   # | m
+d5sum
echo

# older psql doesn't have  --csv  (introduced in postgres 13); in that
+ case use: 
# echo "copy(select * from pm11107044 order by 2, 3) to stdout with (f
+ormat csv, delimiter ',', header true)" | psql -qX
[download]

Output:

./pm.pl 
-- unordered data.txt:
CAT_HEADER,SUPPLIER_CODE,CUSTOMER_CODE,F4,F5,F6,F7,F8
CAT_LINE,0001P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0002P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0001P,ABC23456,20190924,,1,Z,2.24
CAT_LINE,0002P,ABC23456,20190924,,1,Z,2.24
CAT_LINE,0001P,ABC34567,20190924,,1,Z,2.24
CAT_LINE,0002P,ABC34567,20190924,,1,Z,2.24

-- ordered data:
CAT_HEADER,SUPPLIER_CODE,CUSTOMER_CODE,F4,F5,F6,F7,F8
CAT_LINE,0001P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0001P,ABC23456,20190924,,1,Z,2.24
CAT_LINE,0001P,ABC34567,20190924,,1,Z,2.24
CAT_LINE,0002P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0002P,ABC23456,20190924,,1,Z,2.24
CAT_LINE,0002P,ABC34567,20190924,,1,Z,2.24
[download]

( Another (actually more appropriate) database way would be to read the data file directly as text via file_fdw. Maybe I'll have a go at that tomorrow. )

Edit: I just realised that --csv is in postgresql 13 -- the alternative for earlier versions is mentioned ( COPY (select ...) ... )

What came to my mind was to use Data::Table. It will import from a CSV, can handle a header row, and it can sort by one or more columns. If I understood your post correctly, then it looks like this module will do everything that you're wanting to do.