The OP has not been back in the last 4 years, so here is a short answer that can be expanded if ever of interest.
All the existing answers are wrong.
This is entirely doable.
Issues are mass & range, speed, temperature & safety,
In about that order. Perhaps :-).
A flash-boiler, alcohol or kerosne fired, and a burner plus a water supply will generate steam, able to generate powers in the fractional to few horsepower range, either with tiny lightweight reciprocating motors, or by steam rocket.
Wheels are an issue- but sensible engineering can create wheels able to handle surfaces of the day. I'll levae that to others to fill out.
A "flash boiler" will convert thermal energy to steam at low to medium pressure at acceptable mass and energy levels in this context.
Hydrocarbon fuels have acceptable mass and volume energy densities.
A litre of ethanol or kerosine have energy content of very roughly 10 kWh / litre or kilogram (higher for kerosene) and delivered energy as steam in the say 1-3 kWh /litre range.
A "Flash Boiler" (FB) consists of a coil of pipe (usually copper) heated by an external source - here a burner, with pressurised water introduced appropriately
Even at 1 kWh/litre say 5 litres of fuel will provide 5 kWh - say 1 kW for 5 hours or 5 kW for 1 hour or ... .
The main limitation once safe (if not sane) operation is achieved is liable to be water capacity. Steam generation requires about a gram of water per 2 kW seconds of steam generated. So a kg of water produces about 2000 kg-seconds of steam. If a rocket is is used (see below) assuming delivered "vehicle power" in the say 1% - 20% range or 20 to 400 kg seconds per kg of water.
While small model reciprocating engines are well known (see below) powers in the HP + range are able to be delivered directly by direct steam rockets. Achieving this does not require rocket science in practice, only in theory :-).
A steam rocket need be neither extremely large or heavy. Being strong enough to deal with peak pressure out of the flash boiler "is a really good idea".
Flash steam to reciprocating engines for models delivering powers in the HP range are well known:
How to build flash steam generatos and related steam enines here
Includes page 23-53 full detail for building a model aircraft engine weighing 3/4 ounce and delivering 1/4 HP to a propellor. 60 psi operating at 3500 RPM :-) . Steam generator weight not stated but probably well underone pound. That's about 200 Watt delivered, or about the power of a very low end ebike. Propellor optimisation would allow low velocity vehicle operation.
Page 34 - Hydroplane. 1 HP+ delivered to prop. 30 mph max speed. Top models achieve 120 mph+
Flash steam based model hydroplanes - 120 mph. 20cc steam engine ! here
Wikipedia - steam rocket
A HTP (Hydrogen Peroxide) rocket can deliver about 300 kg-seconds per kg of HTP using silver-catalyst screens and 85% HT P (the upper limit for silver due to screen melting). The early HTP rocket packs delivers 17 seconds of flight. A say 10 kg propellant load would deliver say 300 seconds at 10mkg thrust. Hydroghen Peroxide would have been able to be synthesisedsd and concentrated "back then". First produced 1818 - Wikipedia. 100% HTP delivers 440 kg-seconds pere kg.