As I mentioned, my grandson has a couple of toy cars, that are capable of driving up a flat vertical surface, or even across the ceiling - they're powered by two AA cells, I don't see AA cells lasting very long powering an 11.76W load.
The challenge as I see it, is maintaining sufficient traction - the car can't climb the wall unless it has sufficient traction - my grandson's toy does it through what can be considered a "reverse hovercraft" principle - a thin flexible rubber skirt just long enough to bridge the gap between the chassis of the car and whatever flat surface it's on, and a fan to create a vacuum to pull the car against the surface.
The weight of the vehicle is obviously going to be a critical factor.
Is RC Remote Controlled or Radio Controlled? My grandson's toys are radio controlled, so self contained, but you can do remote controlled using a wired controller which would enable you to put the power source in the controller, thus reducing the weight.