First up, you should really use a module for handling your tab separated data. Next, think in terms of read a record and print it. Then you get something like:

#!/usr/bin/perl
use strict;
use warnings;
use Text::CSV;

my $csv = Text::CSV->new({binary => 1, sep_char => "\t"});
my @headers = @{$csv->getline(*DATA)};

while (my @data = @{$csv->getline(*DATA) // []}) {
    print "$_\t", shift @data, "\n" for @headers;
    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]

Prints:

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]

The @{...} stuff turns the array reference returned by Text::CSV::getline() into a list. The // [] bit in the while loop suppresses a warning by turning the end of file undef into an empty array.