My 5 year old is a great range buddy. We'll drive around the club I'm a member of, and find an unused range, and set up. He's well versed in when we can walk forward, and when we stay back. I dont like to use a range with other shooters on them out of consideration for his safety, and the nervousness of other shooters. He'll hop on my lap on the bench and take a few shots with a .22 bolt action sometimes, but he's pleased as punch to draw targets with a big marker, and walk out with me and staple them up.
If we dont find an empty range, we just grab a soda, put in our earplugs and watch the guys shoot skeet at the trap range.
Big deals for keeping them safe, happy, and interested so far seem to be to just take them when they ask, don't pull them away from something else to go. If they get tired of being there, pack it up and go home. My son understands that if he doesnt listen and do what he's told even one time during a range visit, we're going home right then and there. We haven;t had that problem. I gave him his own glasses and hearing protection, and a small range bag to keep them in. He also has a stack of printer paper and his big marker. He is also sadistic in target choice. We have a little plinking range, and he sets up spent pistol casings for me at 20 yards. I shoot em with a scoped .22 from sitting with a sling and rarely miss. He is underwhelmed by this feat, and harasses me greatly when he sets up 10, I run through 2 5 round mags and theres still one standing.
Oh, and handwashing. Lots of it. You dont want them wandering around with primer lead residue on them. Just keep them happy, comfortable and safe.
And don't fuss when their momma teaches them how to make crafts with fake flowers
Well rounded, you know.
Edit:
Oh, and one more tip for a first few range visits. While you are shooting, ask them to put their hand on your shoulder, that way you know they are still behind you, and not potentially wandering into danger. You stop feeling that hand, safety goes on, head comes up.