the way ive heard is go into create a pet thru CAS and create the dog or cat or pet you want, then when its saved like a normal sim, you can merge it with the sim you want to give a pet to
If you are not opposed to cheating (I am not, I am a big cheater pants don't hate lol) you can enter the testingcheats cheat and shift click the pet you wish to change and select edit sim.
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Is there also anyway I could edit my pets looks (choosing breed, etc) like in Create a family without losing my current sims?