What is the best type of pet for her cause we need to know what type of pet she can take care of?

An 11 year old should be able to take care of most all kinds of pets, but there are other factors. One is what kind of pet the child would like to have, and another is where you live (city, country, busy road, house, apartment, etc). Another is how much time the child has to give to care of the pet, especially before school and right after, if sports and lessons and so on are part of a busy schedule.
So I would sit down with your child and start talking about all of this over several days and maybe weeks, because it's an important and serious decision. If you haven't had experience with puppies and dogs, I would think twice before getting one, because they require the most attention and training. Maybe a cat, hamster, gerbil, or parakeet.

Guinea pigs make good first time pets..

A tarantula!

Ok, kidding... although they do make great pets.

My daughter had a mouse. A little white mouse from the pet store and that seemed to be a great pet for her. Easy to take care of, fairly cheap, she even thought it was cute.