Well, an easy way to do it would be to map the month to a quarter with an array:

my @quarter = qw(q0
   q3 q3
   q4 q4 q4
   q1 q1 q1 
   q2 q2 q2
   q3);
# Later...
@sorted = sort
    { $quarter[(split(/\//, $a))[0]] cmp
      $quarter[(split(/\//, $b))[0]] }
        @rawdates;
[download]

Just to clarify, the split breaks up the date strings into components at forward slashes, and the [0] pulls out the month part.

Note: I'm assuming all the dates are in the same year, although it shouldn't be hard to extend this to sort on year also.

HTH