Reddit mentions of Philosophy and the Young Child (Harvard Paperbacks)

Alison Gopnick would be a good philosopher to investigate to answer these questions—iirc she's the leading person right now in this area. The only book I've read on the topic is Philosophy and The Young Child by Gareth Matthews. It was really good and will give you lots of ideas. One that stood out to me was that when your child asks a question (the example was something like, "why do we have two eyes?") instead of just giving the answer, ask them what the purpose could be or other leading/Socratic-style questions, until the child reaches the correct conclusion by themselves.

For more literature suggestions, I'd look at the bibliography of this SEP article.

Often what's used by outreach centers and philosophy for children programs is using children's literature that have philosophical themes and then asking questions about the various themes. I know that The Phantom Tollbooth is a favorite among many philosophers who work in outreach.

Another thing to do would see if the philosophy departments in your area have outreach programs (specifically philosophy for children outreach), and see what they typically do during their outreach.