I wouldn’t get a kitten for an eight year old because:
They bite, not deliberately but in play
There are no guarantees that the kitten is going to be a good pet for her. It might not like her, might not be a sociable cat (not all of them are).
A kitten is only realistically going to stay a cute kitten for a few weeks/months and then it’ll be an adult cat who may in fact prefer the outdoors to staying inside with the child it was bought for.
Added to which,cats can do damage to the house, climbing the walls (literally in some instances, scratching the furniture, climbing the curtains, and that’s before you count bringing home dismembered dead (and sometimes not dead) animals and birds for you to deal with.
Then there’s the cost. Neutering/vaccinations/micro chipping, and that’s before any potential health difficulties and will set you back a couple of hundred quid as well as the price of the kitten.
If you still want a kitten after all that then at the very least a rescue will probably charge you around £75/100 for each kitten and that price will include vaccinations/neutering/micro chipping.
Cats live for around 15/18 years but the average is actually much lower because of the sheer number that are killed on the roads.
And your DD will probably be married with children (and kittens) of her own before this one dies.
I would only get a kitten if you want one.