Adding qu| at the front of $1 and removing q from [...] provides support for the "qu" combination.   My first attempted tweak was to add (qu) inside $1's [...] but that hosed things for words like "jumped".

Bonus points for guessing the cliche phrase I tested this with.  <grin>

#!/usr/bin/perl -w
use strict;
while(<>) {
    s{ \b(qu|[bcdfghjklmpnrstvwxyz]*)([aeiou]+)(\w*) }
     { if($1) {$2.$3.$1.'ay'}
       else {$2.$3."way"} }egix;
     print;
     }
# END
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    cheers,
    ybiC