Tim,
I have a 4-year-old daughter who goes out with me occasionally to the course. Our routine seems to be:
(1) Go to the practice bunker, set up my giant golf umbrella in the sand, let her play "beach" under it while I hit a few bunker shots,
(2) Cart ride to the 17th hole, which has a waterfall and a ledge overhanging a lake. Have a tee race down the waterfall. Tell (and retell) her the story of the one guy who got too close to the edge and fell in,
(3) Ride back to the putting green and hit a few putts (she has a putter), then I keep putting while she goes to the cart and draws on the scorecard,
(4) Go to the range and hit a few. Let her hit her putter off a tee. Set up the umbrella on the range and let her fill divots with sand while I hit a few more,
(5) Cart ride to the 12th hole, a par 5 that borders a ranch all the way down the right side. There are cows there, but we look for the 2 donkeys so we can feed them grass and weeds through the fence.
Last time we actually went out on the course and I played 9 holes. She didn't want to leave, so that was encouraging. I don't know how long it will be before she wants her own clubs, but I think she's at least hooked on being out there!