Hello, you need to normalize somehow your data before elaborating the results: infact you have at least 2 field of two separaated words and at least the value of the name of the keeper with a space (the code below is broken for a keeper named just 'Tarzan' as for one named 'Vladimir Ilyich Ulyanov').
You can practice splice to modify the fields outside the loop, considering just the first line. In the loop you'll join firstname+lastname to have a singular field for them.
After this sanitazing work, the game is simple. I leaved some helpfull debugging print statement commented, to see how splice works (i not use it so often...)

use strict;
use warnings;

my @fields = split /\s+/, <DATA>;
   # print "BEFORE: ",(join '|',@fields),"\n";
my $prem_et = $fields[7].' '.$fields[8];
splice @fields,7,2,$prem_et;
my $nd_al = $fields[8].' '.$fields[9];
splice @fields,8,2,$nd_al;
   # print "AFTER: ",(join '|',@fields),"\n";
while (<DATA>){
chomp;
      my @entries = split /\s+/,$_;
            # look at @entries before joining the name
            # print +(join '|',@entries),"\n";
      my $name_with_space = $entries[1].' '.$entries[2];
      
            # see the doc for splice: we remove item 1,2 and replace t
+he with a single
            # $name_with_space
      splice @entries,1,2,$name_with_space;
      
            # UPDATE for null age
      @entries = (@entries[0..4],'',@entries[5..$#entries]);
            # but since we learn 'splice' we can do with it too:
            # splice @entries,4,1,$entries[4],'';
      
            # look at entries after splice
            # print +(join '|',@entries),"\n";
            # foreach index of entries we print both corresponding fie
+ld and entry
      print map {"$fields[$_]\t$entries[$_]\n" } 0..$#entries;
      print "\n";
}

__DATA__
Animal    keepers    M/F    YEAR    DOB    AGE    FSM    PREM ET    ND
+ AL    EAL
GIRAFFE    JAMES LE    M    9    10/12/2007        Y    Y    N    N
HIPPOS    JACKIE LEAN    F    6    11/12/2007        Y    N    Y    Y
ZEBRAS    JAMES LEHERN    M    3    12/12/2007        N    N    N    Y
LIONS    AMIE CAHORT    M    1    13/12/2012        Y    Y    Y    N
[download]

with the output:

Animal  GIRAFFE
keepers JAMES LE
M/F     M
YEAR    9
DOB     10/12/2007
AGE
FSM     Y
PREM ET Y
ND AL   N
EAL     N

Animal  HIPPOS
keepers JACKIE LEAN
M/F     F
YEAR    6
DOB     11/12/2007
AGE
FSM     Y
PREM ET N
ND AL   Y
EAL     Y

Animal  ZEBRAS
keepers JAMES LEHERN
M/F     M
YEAR    3
DOB     12/12/2007
AGE
FSM     N
PREM ET N
ND AL   N
EAL     Y

Animal  LIONS
keepers AMIE CAHORT
M/F     M
YEAR    1
DOB     13/12/2012
AGE
FSM     Y
PREM ET Y
ND AL   Y
EAL     N
[download]

HtH (animals too!)
L*
UPDATED: i've not noticed you also have the age value empty! i've corrected the above.