I was going to recommend a rabbit, also.
Rabbits enjoy eating fruit tree and
rose prunings. It's important to the rabbit's health that it chew on
wood, so you teach her about animal care and pruning at the same time.
In personality I've always found them to be most like cats, though they take better to a leash. You can train them to use a litter box so they can run around rooms with hard floors. The hard little pellets are uncontrollable but on a hard floor you just sweep them up, it's one of the great things about rabbit droppings. The other one is that they can go directly on the garden without worrying about smell, disease, or burning the plants.
The real key to this working is taking time and attention to socialize the rabbit. Especially as this is her first time with a rabbit, take the time to find the calmest rabbit you can. Talk to the rabbit and handfeed it treats. Those rose and fruit tree prunings are great, too many carrots are like too much cake for a kid.
In dietary needs, get lots of real
hay. That
should be the bulk of the diet. They need all that fiber to keep their digestive system flowing smoothly. That could easily be the most common way pet rabbits die is people feeding them too many rich foods (vegetables, pellets, and treats) without
enough roughage. The wood and hey also keeps their teeth in good condition so you won't end up with a dentist visit for a pet.
I know, you haven't decided on a pet yet. I just think it can help the decision process to have enough information while you think.