Why not start a separate project for your pets if it is your pets pedegree you want to record.
Or, under Facts for a person you can add your own Events and that could be I.E. Pets.
If it is all your ancestors you want to add pets to, I think you can only record a generation or two back in time before all records are missing. To add such function for so little information would be a waste of developing time when so much other things need to be fixed.
By the way I loved my Birman cat Musse whom I had for 17 years and now I have Cornelis and Felicia who are also Birman cats.
I love my pets as if they were my kids, but I would absolutely and unequivocally and vehemently oppose any such action! Family trees are about human descent and other family connections by blood or adoption or marriage or other human partnerships. Pets can be honored in other ways, in pictures for instance. Or they can be included in family tree identifier pictures with their human guardian.