When you run the code you wrote through the debugger you will notice that it executes the our ... statement after the subroutine has run. Some simple repositioning of code as this,

#!perl                                                      
package My::Test;

our $VERSION = 1.11;

package My::Test::Print;

our $VERSION = 1.2;

sub printer {
        print "This is ". $My::Test::VERSION ."\n";
}

package main;
my $test = 1.23;
print "test: $test \n";
print My::Test::Print::printer() ."\n";
1;
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Makes this output:

test: 1.23 
This is 1.11
[download]

Note that I took the liberty of adding a VERSION in each different package which I think is what you meant to do.