Hey, So on my account I have a lovely ladybug, trying to get a noble kookaburra. I trained it to Adult a while back as tried to breed it recently. I got 8 Ladybugs back and not a single other pet. I then trained one of the higher pedigree ladybug babies up to ancient. I tried 2 more times and still to no avail. My lovelyladybug is now at 76(21). I have tried breeding with anything from high pedigrees to low ones, most recently failing against a Noble Kookaburra at 68(8)...
If the pet is restricted to a school (I don't know if ornery kookaburra is) then I believe there is a much higher chance to obtain the pet you want if you're hatching on a wizard that shares a school with the pet. Not sure if this is true or not but it seems to happen to me. Might be pure coincidence.