Yes, and the thing with cats is, they'll decide who their key human is - sadly there's no guarantee it will be your DD OP! Fickle isn't the word... The cat could totally bond with your DD and that would be great but equally her routine (the cat's that is) might be to go out after she's had her tea at 5pm and not come in until the next morning, or spend all her time sitting in a certain spot quite clearly not wanting to be in the room where your DD is - you'll never know in advance what type of cat you're going to get.
I would also strongly recommend that whatever you end up with, you obtain that animal from a rescue. Parrots for example yes, amazing pets, but these are pets for LIFE - 30-40 years.
What would happen to all the unwanted rabbits, guinea pigs, rats, hamsters, cat, dogs if people didn't rescue them from rescue centres (and bring them home to a life of 'torment' in a cage')? They'd all be PTS. I get what people are saying about cages not being adequate in size but that's down to you personally to provide the correct size cage so you don't have that problem, and with ALL pets no matter what species, stimulation, acute attention to detail on how to care for that animal, constant handling - all of this is part and parcel of having a pet. We have two guinea pigs (piggies shouldn't be homed solo) in a large indoor cage, they have a lovely time since their main purpose in life is to either be eating, sleeping, pooing or weeing. They come out regularly for general cuddles and handling, floor time, we have long
and very important conversations, hand feed, groom, trim their nails, the odd bath in the sink (for they are widdly long-haired piggies), and they are eminently happy.
If you can afford it there's no reason to rule out taking on a rescue dog as you do have the option of having someone come and dog sit or dog walk during the day say late morning, then DD would be back in time from school to take the dog out again - so if you could manage that then ruling out a dog may not be necessary.