Works for me:

mucn13154:~/tmp 1 502 $ touch "has space"
mucn13154:~/tmp 1 503 $ perl -lwe 'use File::Copy qw(copy); copy("has 
+space","has more space")'
mucn13154:~/tmp 1 504 $ find . -name 'has*'
./has space
./has more space
[download]

If you try my example on your perl, what error message do you get? Which version of Perl, respectively File::Copy, are you using?