The type of engine would depend, to an extent, on three things.
1. Physical size/shape - will it fit into the available space under the 'cowling', whilst allowing convenient connection/paths of drive shafts?
2. What is it required to drive and how?(eg. prop only, wheels only, or both).
3. Overall weight and power. Will the aircraft structure bear the weight, and will the power do what is required, without stress damage to the aircraft structure?
The engine is going to be virtually a 'stand alone' item, with all the power and torque being transmitted to whatever drive train is used, and to the replica airframe (maybe that should read 'ground frame?!), which, I suspect, would set-up quite a vibration in the framework, as, unlike a car, there would not be any heavy engine supports, or a solid drive train and gearbox, plus the damping effects of a chassis or monocoque, to absorb some of the stresses involved.
Remember also, in order to propel the replica purely from the action of the prop, the engine would have to be fairly powerful, and controllable via a basic throttle arrangement. More importantly, the prop itself would need to have the required pitch, to provide motion, whilst at the same time being strong enough to absorb the power delivered to it, without shaking itself to destruction, or worse, shedding blades in all directions.
A realistic- looking prop can be made from glass fibre, but it's doubtful that this would propel the aircraft replica on the ground whilst retaining structural integrity. It would, however, probably be fine if just rotating via the drive from a small engine, under a low power loading, again with throttle control, with motive power being supplied, via a drive system to the wheels, from a larger engine.
Or, the larger engine providing motive power, and rotating the prop by a system of reduction gearing, but then that's complicating matters.