Not quite so small or simple.
You need tank, engine/generator, exhaust system plus pollution control, new safety tests, and a path to route the exhaust.
What would you need an engine or generator for? We're talking about a heater.
This is a very small device, less than a cubic foot which burns about 1/6 gal/hr so, as noted, a 2 or 3 gallon tank would be plenty. The exhaust is relatively cool, around 150 F and would be only a couple of inches in diameter. The heaters are already CARB compliant as they are in common use in trucks, airplanes and boats. Based on how DOT regulates much larger auxiliary fuel tanks for pickups, I doubt there would be any requirement for new crash tests etc., especially if it burned diesel fuel.
Diesel would likely be the fuel of choice since it doesn't degrade over time the way gasoline does and evaporates much more slowly. Alcohol is an interesting idea, but methanol has about 2/3 the energy density of diesel and ethanol less than half, so either would require a somewhat larger tank. I'd think the biggest issue would be that neither is readily available on the road which is where you'd need it, so I still think diesel would be the best choice.
I'm surprised that Estonia would prohibit auxiliary heaters in electric vehicles, the US EPA doesn't AFAIK, they even give the full credit to the BMW i3 with a range extender motor/generator. Are other things like the use of windshield anti-freeze fluid containing ethylene glycol or isopropyl alcohol in electric vehicles prohibited as well? Those are petroleum products and just evaporate into the air, they're not even broken down by combustion. Anyway, if you don't want one, don't order it.