A non refers to any of these 4 dogs:
Nonswirl, Nontag, Nonjewel, and Noncoon. These are all OMGSR dogs
The nonballoon is not a non dog.
Each non goes for 10-12 midadvents, 1 midadvent is 7-8 2009 rares, more commonly 8 '09 rares. One non can also get 2 sorbets.
These values aren't solid and everyone follows different values, but these are the most commonly followed values at the moment, in case you plan on trading up/down these pets in the future!