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I'd say rat or goldfish. If you get a "feeder goldfish" they can be incredibly inexpensive (as in $0.10 to $0.25 each), and can be quite hardy. In the past I've kept a couple in a 1+1/2 gallon tank with no filter, heater, or aeration for several years. And if she mistreats it and it dies...well, it was a feeder goldfish, that is it was intended to be fed to a carnivorous pet fish, so it's not like it had a long and happy life ahead without her.
If she wants something she can hold, then a rat is probably about the lowest maitenance you can get. And the lifespan is shortish, so if she gets bored and ignores the animals, the parents won't be stuck caring for a pet they don't want for all that long.
Russian Box Tortoise. You only need to feed them every other day and clean their living space once a week. It's also cool to let them wander around the house or yard. They're about the size of a softball and can live 50-100 years!
We recently made the same decision a year ago with my daughter. Here is our experience:
I heard that hamsters could bite and guinea pigs were a bit delicate. So, we decided to go with a rat UNTIL I looked at them in the store and I just couldn't do it. (i'm sorry, I'm ratist)
The pet shop owner suggested mice. He had a cage of them and they were very friendly, you could hold them and they didn't bite and they were cute.
I read up on mice prior to buying. Mice are social animals and it is cruel to get only one, so we decided to go with two.
Sadly, they were not the same sex like the pet shop owner assured us and a full four months after we bought them the one had babies. The babies all died immediately and the mother died that day.
That day was a miserable day in our house.
Well, since the other mouse was a male, we couldn't get a companion for him because the males are very territorial. I read about acclimating him to another mouse and it was just way more work that what I was willing to take on.
So, Fudgie lives alone, I guess his life is better than it would have been had we not bought him because he would have been snake food. However, ever since Peanut died Fudgie has gotten a little grouchy. He does bite now and he chews his cage bars incessantly. It's a bit sad. But, my daughter loves him and plays with him. We put him in the ball and she sets up obstacle courses for him. She has a pair of gloves that she wears when handling him so she won't get bit.
He isn't a lot of work, you have to clean the cage once a week. I will say that the cage is stinky, even when you clean it, it just stinks. It doesn't stink up the whole room, but no matter what I clean it with, it smells.
My daughter now wants a rat and I think we might go for it next time. She's been a good owner to poor, lonely Fudgie.
Other suggestions: My eldest daughter had a beta fish in her room in a small aquarium. It was a nice companion for her at night. It was a night-light for her.
A fish might be good practice for your daughter to show she's responsible enough to take care of a bigger animal. Beta fish are nice because they are pretty, they don't need to be fed often, they don't need heated water and they can do very well in water without a filter.
I've had birds and I think a bird is a step up in commitment from a rodent. We loved all our parakeets, they are highly entertaining.
Children love rabbits, but this doesn't mean they should get one.
I've heard just one time too many about another case of a post-Easter dead bunny which was mishandled by a kid unaware they are holding a living animal, not a plushie. Bunnies don't like to be held, carried and they WILL kick and bite if mishandled. Those hindlegs are powerful, btw. Not to mention that pet shops tend to sell baby rabbits who often aren't even a month old and need VERY special care and food to survive.
IMHO a 6yo isn't really capable of handling a fragile creature like a rabbit. A dog or a cat could handle kid "abuse" much more easily. A bunny can't. They are quiet, tame creatures who crave peace and gentleness. Also, they require as much care as an average dog or a cat, and their lifespan is quite long - it can be over 10 years, if cared for properly.
Bottom line, I don't want to be a grouch, but mishandling bunny rabbits is VERY common, especially because they appear "small and cute", they are cheap and are bought VERY frequently by tardy parents. I'm not saying DON'T buy a bunny, I'm just saying that if you do, I hope you will be responsible with it.
P.S. Contrary to popular opinion, a bunny cannot survive on its own in the woods. If you decide that it's too much work and you won't to get rid of it, the cruelest thing you can do is leave him alone in the nature. People who do that just sentence the poor animal to slow, painful death (unless the creature is lucky enough to get killed by a predator quickly).