Burrill Lake, east of the bridge, has a nice sandy bottom. Depth is about 1 metre at best, and the area is quite small, so would be perfectly safe for introducing a 7YO to the sport. Might be too small.
West of the bridge is very protected by the surrounding hills. The winds swirl around, making it counter-productive for teaching.
Cannot help you with Tabourie. Must have a look at it myself, one day.
As Jase says, SP is the go.
In a lighter day, Hyams Beach, in Jervis Bay, is also great for learners. If the prevailing NE is strong, Hyams gets quite a swell. Hyams reputedly has the whitest sand in all the world.