Several structures are possible. I've used a HoHoA here. You might want to strip spaces from the hash keys if you have to make many references to them in your code.

#! perl -slw
use strict;
use Data::Dump qw[ pp ];

my %data;
chomp( my @L1Headers = split "\t", scalar <DATA> );
chomp( my @L2Headers = split "\t", scalar <DATA> );

@data{ @L1Headers } = map{
    +{ map{ $_ => undef } @L2Headers[ 0, 1 ] }
} 1 .. @L1Headers;


while( <DATA> ) {
    chomp;
    my @values = split "\t";
    for my $l1 ( @L1Headers ) {
        for my $l2 ( keys %{ $data{ $l1 } } ) {
            push @{ $data{ $l1 }{ $l2 } }, shift @values;
        }
    }
}

print pp \%data;

## "What's Data Set 1's y value at Data Set 3's x3 value?"

for ( 0 .. $#{ $data{ 'Data Set 1' }{ 'X units' } } ) {
    $data{ 'Data Set 3' }{ 'X units' }[ $_ ] eq 'x3'
         and print "DS3-X == x3, DS1-Y == ",
                $data{ 'Data Set 1' }{ 'Y units' }[ $_ ];

}

__DATA__
Data Set 1    Data Set 2    Data Set 3
X units    Y units    X units    Y units    X units    Y units
x1    y1    x1    y1    x1    y1
x2    y2    x2    y2    x2    y2
x3    y3    x3    y3    x3    y3
[download]

Outputs

c:\test>junk2
{
  "Data Set 1" =>{ "X units" =>["x1","x2","x3"], "Y units" =>["y1","y2
+","y3"] },
  "Data Set 2" =>{ "X units" =>["x1","x2","x3"], "Y units" =>["y1","y2
+","y3"] },
  "Data Set 3" =>{ "X units" =>["x1","x2","x3"], "Y units" =>["y1","y2
+","y3"] },
}
DS3-X == x3, DS1-Y == y3
[download]