Cat or dog is the most suitable or fish.

Search for small size cat/dog breeds.

Small fish like guppy and tetra. Goldfish is small and beautiful but it is not for newbie.

Make sure that you learned all the basic before hand as fish is not as easy as you think at first.

The fish tank require regular maintenance and a reasonable sized tank even for small fish.

For eg. you need to change half of the water of the tank every 2 week. Full water change every half year. Good water filter system and etc.

Only go for it if you are sure you can take over if your daughter losing interest.

Read this guide/FAQ
https://www.reddit.com/r/Aquariums/wiki/index/

Other small pets to consider are sugar glider and hedgehog. Do search and read the pros and cons first.

As a past owner of a turtle and hamster i would advise you against it unless you can stand their habitat smell.

Probably better to get a sugar glider or a guinea pig.

Sorry, cannot agree on the hamster part. But I will say that they will bite only when startled/threatened and scared. I've had a couple of hamsters before, one after another. 2 died of old age while another escaped because someone left the cage open. 
Never once was I bitten by them. They even eat food off my fingers. 
I believe most importantly is to have them be comfortable with your presence and scent, then they need not be scared of you touching them.
Same goes for any domestic animal, I guess.

So, TS, hamsters are nocturnal animals. If you don't mind your daughter staying up late a bit just to play with them, depending on what time is her bed time of course.

rabbits.

9 years old? Old enough to be responsible for taking care of a pet? 

https://petrock.com/

I don't know if a fish will make her feel any less lonely though as they are not interactive. Cats and dogs are you best bet but since it's not plausible, hamster or guinea pigs are next best options.