I think sometimes child actors actually can give a less believable performance than a child who isn't necessarily trained. Child actors go to their acting schools and get taught to do this and that, but in the end I feel like there can be less believability in some children who have been trained vs those who haven't. That said, you need to be the kidn of Director who can work with a child that has never acted before.
THere are all sorts of things to think about when making a film with children in it, so make sure at least your Producer and 1st AD have police checks and state that outright. There are often certain laws that affect how long a child can work on set for without taking a break (ie in Aus, ages 6-9 can only work for a max 6 hours, 9-12 max 8 hours etc) and how long they can have off school without employing a tutor. Make sure you are across these. You also want to hold yourself and the set to high professional standards, so that means no swearing in front of the kids etc etc.
In terms of finding the kids to go in it, go and see some junior theatre productions, including high school plays and musicals, go to local schools and check out their drama department (all with permission of course, you don't want to be that creepy guy..). You may even also find that contacting some of the kids talent agencies can be useful.