It depends on your campaign. It also might depend on the other players and the motivation of this player to choose a "child" character.
Keep in mind also, your campaign may be set in a medieval setting and as far as I am aware, very few children were educated and most were expected to start working to support their families (helping around house/farm etc) as soon as they could walk.
This wiki article cites the age of 12 for girls to be considered "adult" and able to marry for example.
https://en.wikipedia.org/wiki/Childhood_in_medieval_England
http://www.representingchildhood.pitt.edu/medieval_child.htm
Since the player wants to play a "prodigy" then with the appropriate background and stats it might be reasonable assuming everyone else at the table doesn't mind but I would lean toward the higher end of the age range of 12 or 13 when the person could be considered a young adult, might have been apprenticed between one and two years prior and might have acquired reasonable training. It is hard to picture an eight year old with the requisite training and they would certainly be physically much smaller (assuming a human baseline ... and not some sort of demigod background).
As for story line ... there are many many possibilities. If the party enters the jungle with some urgency and the person stows away in baggage or disguises themselves in some way (depending on class and skills) then it could work since the party would be loathe to turn back to return them to the city.
However, given how hot Chult is there is no way the character could survive for even a couple of days in some sort of baggage without water .. even then I don't think that would really work. The better approach would be to pretend to be older than they are using Deception or a disguise of some sort. Mechanically, as long as the character proves to be competent at their chosen role/class then the age is just a role playing aspect to the character which can easily be worked into the plot.
As for children having adventures ... literature is full of them (especially young adult fiction) so that isn't really out of the ordinary either.
The real issue is whether anyone will be bothered if the child/young adult dies in the adventure or suffers in some way (mummy rot/other jungle diseases/tortured by an evil villain). Some players might find that sort of scene to be more emotional than they like since they might find that they empathize more with a child character than others and THAT might be a problem down the road for the campaign ... which is why you might want to get a buy in from the other players.
As an example, I watched a stream of Mike Mearls running a module for a group of folks including Chris Perkins, Matt Mercer and others (. One of the characters was a 12 year old halfling champion fighter played by a woman in the group. Unfortunately, this character was the only one who died, disintegrated by the eye of a beholder. Personally, I found that a bit disturbing.
https://www.youtube.com/watch?v=XlAEYxu8L84&t=4220s (about 1:24:30)
