Is this for school? I had to do one in year 8. Mine won at my school, so I got to go to a completion against about 15 others schools. It was good, because I got to go during school time. I think I came about 5-7th out of about 15-20 or so, I think.
It was a 15 metre race, we had to use the mouse trap we were given, and it had to be less than 500mm long I think.
Mine was long (close to 500mm) with some cardboard wheels (they were bought round, mum had them for putting cakes on) that were about 200mm in diametre. The top few cars had CD's as wheels.
You've got the right idea of using a long lever attached to the spring, but you want the axle to be behind the end of the pop stick when you have it fully pulled back, otherwise there will be some slack in the string when you let it go.
I had a thin aluminum tube for the axles, with a small hole drilled in the centre of the rear one. I put a small bent nail in the hole for the string to attach to, just make sure the nail comes out of the hole when it gets to the end others wise it will lock the axles up. Make sure to wind the string up tight and in a way that it won't get tangled.
Use bearings on the wheels. Have the rear wheels connected. Put the string in between the rear wheels, not on the side, so the string doesn't interfere with the wheels. Keep it as light as possible.
The main things you need to change is to make it longer and use bigger wheels, I recommend CD's, especially for the rears, fronts don't matter as much, as long as they roll well and are light.
Depending on the length of the race you might need to tune the length of the pop stick to get the best mix of acceleration and top end.
Oh, and make sure it's not going to tip over in the race like a couple of the others did
I knew that what I learned from mouse trap racing would come in handy one day.