The king charles cavalier spaniel is a lovely temperment for children, and might appeal to your friends daughter as a breed. These gentle dogs aren't known for cat chasing.
We have a rescue cat-tested whippet and she's pretty cat-like in some of her habits. Notably her love of warm, soft places to curl up and snooze in. You don't know she's in the house most of the time. She also doesn't have hugely onerous excercise needs. 2 or 3 x 20min free runs off lead a day (make recal a training priority) and a nice family walk at weekends.
Do ask a rescue for an animal that's been in foster and is cat tested though as our whippy is LETHAL to squirrels, rodents, rabbits and other small furries and the "dog has eaten the cat" is not a good thing to have to share with a child.
Many nice dogs end up iin rescue through things like bereavement, divorce etc. The trick seems to be to find a rescue that does a lot of fostering as they are able to properly assess what a dog is like in a home environment so you'll "get what it says on the tin".
My last dog was a chihuahua - treat em like dogs not dolls and they are smashing. I miss my old git summat chronic. I was just a bit concerned about size and clumsy growing boys when choosing his replacement (esp as some of my son's friends have sens which mean they don't always realise they are being a bit rough). The whippet is large enough for me to see what's happening and fast enough to get out of the way. My chi did NEED a lot more excercise than people would assume from his size though.
I also like the papillon but again they need more stimulation and excercise than people would assume from 1st glance.