Here is a pic of the Dolphin: Dolphin Junior sailboat for sale
It is practically a Sunfish like the one I was sailing in today with 20+ knot gusts in LI Sound. What a ride!
mpickering is right that your body placement on that kind of boat is all important, especially when the wind picks up. There were 2 grown men out on a Sunfish today and it took both of us hiking out to get far enough upwind that we were able to broad reach (45' downwind). We got the hull up on a plane and were just flying along in the gusts. I came back from that sail soaked from the boats spray.
It takes a good sense of the wind and balance to be able to keep a boat like this right side up.
You learned one of the tricks which is to let the sail out a bit in puffs but lean out, hike out and see how that balances the boat as well. The other trick for when the boat starts going over is to turn the tiller (steer) into the wind a little, or head directly into the wind and get into irons (without momentum).
You should also do a capsize drill (if you haven't already) with your boat to practice righting it.
Little boats or dingys like the Sunfish can be a lot of fun. They can often have their challenges too.
I like your challenge: learn how to sail.
Keep going out sailing.