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Considerations
If it has wheels and a body of some sort, you can attach a rocket engine to it and go racing. However, you face five basic issues when shoving a model through the air with rockets: lateral stability (the ability to go in a straight line), vertical stability (the ability to stay on the ground), rolling resistance, weight and aerodynamics.
Locating the Engine
One mistake rocket car builders commonly make regards engine placement. Many builders place the engine at the back, which would seem like the logical thing to do when producing a jet. However, such designs place all of the engine's load on the rear axle, making straight-line stability a tricky proposition at best. Instead, you should place your engine mount just aft of the front axle, at a very slight (one to two degree) downward angle. This engine configuration will make your car more of a "puller" than "pusher" (giving it far more lateral stability), and the downward tilt will place a slight load on just behind the front axle (preventing the car from taking off or nose-diving). Put the engine as close to the ground as possible, even below the front axle if you can. An engine at or below the axle centerline will reduce or eliminate the possibility of a roll-over.
Building the Chassis
Think of your rocket car as a front wheel drive; the rear axle carries very little weight, and is more of a "dead roller" than anything else. The rear axle is like the rudder or tail on an airplane, since it serves more to direct the car than anything else. To keep weight down, the best way to build the chassis is a reverse of the "toothpick" single rail often used for CO2 cars, where the two axles are only connected by a single, thin rail. The longer the wheelbase the more stable your car will be, but the more it will weigh. Use the thinnest possible wheels and smallest bearings for the lowest possible rolling resistance.
Aerodynamics
If you've engineered the engine placement properly you shouldn't need any sort of "wing" or spoiler to keep the car on the ground. Stick with a long, low, tapered nose and a smoothly tapered tail for minimal drag. You could place an adjustable fin on the tail (between the rear wheels) to help keep the car pointed straight, but some very tall, thin rear wheels will do the same thing with less weight and drag penalty.