Reading through WWW::MEchanize again did the trick! Thanks for the obvious but very helpful suggestion!

Here is what I ended up with:

#!/usr/bin/perl -w
use strict;
use WWW::Mechanize;
my $mech = WWW::Mechanize->new();
my $filename = "fileblahblahblah.mp4";
my $url = "url";
$mech->get($url, ':content_file' => $filename );
[download]

Thanks again!