You can have the best of both worlds. Use a combination of randomness and uniqueness to make the output unique. Something like, (and I am building on the code in RE: RE: RE: Randomizing Unique ID? ):

my $ID = $ToBase62->( $$ ) . $ToBase62->( rand( $$ ) ) . $ToBase62->( 
+time );
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Not forgeting to call srand() at some point.
And of course, you can use whatever rand() you want.

Update: Don't bother seeding. Tye explains the internal seed here. Also, see the Base Conversion Utility.