You are correct to be concerned, but I think you have to think this out again! About 20% of all work-place fatalities are triggered by a fall from height. Fall arrest netting is an option in construction or agriculture where there is a need for people to be working at height and specialists are responsible for its design and installation. With respect (and correct me if I'm wrong), an amateur design and a permanent installation are a recipe for disaster. There are too many variables, will the net break, how much will it stretch, how high is it above ground, how heavy is the child, did they fall or did they jump, how well is it maintained, what influence will weather have over time?? What's to stop this adventurous child from thinking that the fall arrest netting was a trampoline?
You need to think about making sure that the child never gets to the edge of the roof in the first place. You need a barrier and you need to make sure that a child can't or won't climb it. You might even consider using the barrier to block all access to the roof and not just to the edge if that's possible. A standard edge protection barrier is 900 mm tall. The barrier should be constructed so that it can't be easily climbed, usually by having vertical bars and the bars should be close enough together so that a child can't slip through them. These details are in the Building Regulations, they apply to stairs, balconies and landings too. I don't know if you have a particular child in mind or not, but if there are children in the family then they need to be told that the area is dangerous and that climbing on the barrier is not acceptable. Many families live or holiday in apartments with balconies and thankfully accidents of they type you mention are rare when there is an adequate design, a bit of common sense and a bit of good parenting in the mix. Good luck with this project.