Proper handholds and keeping in habit of using one-hand for yourself goes a long way to keeping you safe, and I'd encourage you to teach your child that.
One hand for the boat is my kid's mantra. If you have the social-activity pleasant/sailing activity stupid typical 12 foot wide saloon, you might wish to retrofit brass uprights and hip level handholds below. When the kid is down there, get vinyl-covered, velcro-secured pool noodles or other rigid foam-type substance (pipe insulation works) and put it up to her head height around those handholds and uprights. If she takes a tumble, she'll slam into a cushioned pole instead of, say, the corner of the nav station or the edge of the companionway steps. You could even put drawer pulls on the steps themselves (they don't have to hold your weight, but hers). When guests are aboard, remove the cushioning and stow it under a berth, if you care about appearances. It's easy to cover the "leading edges" of cabin cabinetry with split foam tubing, and it's not like you'll be taking on a lot of weight.
In a couple of years, and a couple of avoided trips to the face-stitching clinic, your kid should have the experience, the strength and the co-ordination to avoid most falls and can simply follow your own broken-rib avoidance scheme.
My kid' (five going on six) has already done a header down the companionway, which is why I have given this a fair bit of thought. I am a big believer in swinging around the boat like an ape, figuring that standing upright with hands at one's sides is strictly a dockside maneuver.