one thing that i noticed with pets is they attack only what goes for you, or you're attacking typically.
this means though, that if you target one (using * to do so, i think.) they'll rush toward that target to attack them.
as far as your little girl though, go to derphy, try and buy some kind of jurea swordsman or something, do the mission to help the scientist guy in port kapul to get the gene machine, place it in your house (remove something first to let you do so, if you must.) and then get the gene engineering skill from a trainer, buy a bunch of cheap pets when you can and splice them to improve your skill.
eventually, you'll be able to splice alsorts of things to make tough pets with access to skills and body slots they normally don't have. non-human bodied pets have to be combined with other non-human bodied pets however, to gain an additional body part slot from the 'donor' creature. hence why i have a quickling with full regular body slots.
Just remember, your mage may not be viable for too long, but if you can marry a pet and 'create a gene' you can use said gene when starting a new character, to gain bonus starting skill points and such (i think.) and later use inheritence scrolls (if your lich had anything worth using this for.) to 'inherit' (essentially copy for your character, your lich'd still have it.) any items of value. artifacts, seven league boots, stuff like that's good to inherit.