Fish are great, but most 7 year old girls want to hold their pets, so if she's the snuggle-up type, that wouldn't work too well.
My kids have had just about every animal over the years (and still do!) -- hamsters, mice, rats, cats, dogs, fish, frogs and a rabbit. Rabbits are good pets as are rats, but they require a great deal of maintenance/cleaning, etc. and need large living habitats. Fish are hands-off as are most frogs. Frogs, lizards and turtles carry illnesses that can affect some young children's health easily. Dogs and cats require a whole family's participation.
We found that dwarf siberian hamsters are great -- they're a lot friendlier and they don't nip or bite like the teddy bear and other larger hamsters do. But they are small and your niece would need to be taught to care for it gently. Your niece is at a terrific age for learning about pets though.
And our latest addition was a fancy mouse (a colored mouse, not a white one). She's terrific. She's always friendly, never bites, and loves to be held -- but also likes to play with toys too like the balls they can roll around in, etc. Toys are a great option to consider because your niece will have fun picking out things for her pet and it also makes for great gift giving later on!
Dwarf hamsters and mice are good on their own too, so she would only need one instead of a pair, which makes maintenance a lot easier. The down side is they only live about 3 years -- so you'd have that issue to deal with when the pet passes on.
One word of advice from one parent to another though -- check with her parents first before getting any kind of a pet!