Personally I would vote "no" regardless of whether I had confidence the kid wouldn't be exposed to the dregs of the Internet, for two reasons:
1. LLMs are I think pretty inarguably bad at answering certain types of questions in a factually accurate way, at least without nontrivial prompt engineering. I don't think many 8 year-olds will recognize which types of questions the LLM will give inaccurate answers to, or be ready for the sort of prompt engineering that'd be required to mitigate this.
2. Learning is of course more than simply obtaining and memorizing facts. You don't want to overfit your kid - you want them to have to struggle a bit for their understanding so that it generalizes. Sure, formulating questions is part of that process, but there's something to be said for having to sift through pages of search results (or even better, from a learning standpoint, searching through the pages of a book they had to find on a library or bookstore shelf). It's like the old idiom, give a man a fish and he eats for a day, teach a man to fish and he eats for a lifetime. Better to teach your kid to fish (and for knowledge/understanding, not mere facts).
As for image generation, I suspect you'd find more inappropriate content come up there than with a chatbot - and teaching the kid to draw, paint, etc would probably be better for their development.