You have to specify the whole URL so

my $response =LWP::UserAgent->new->get("http://www.mydomain.com/myperl
+script.pl?var1=1&var2=2");
[download]

should be what you want.

UPDATE:
If you just want to run the script, then LWP::UserAgent may be overkill. LWP::Simple will probably do what you want.

use LWP::Simple;
my $data = get("http://www.mydomain.com/myperlscript.pl?var1=1&var2=2"
+);
[download]