I agree. The Fighting-Rabbit-Routine is ridiculous and boring. The devs have done such a fine work evoking the spirit of the New World but they forgot the TRAPPER. The fur trade is such an important element of the colonial era (http://en.wikipedia.org/wiki/Fur_trade). The whole french colony in Quebec was founded on the fur trade and nobody ran around actually shooting or bashing beavers or bunnies to death. They set traps. Easy, safe, efficient.
So, how to do it: Develop a skill tree with trapping branching of somewhere. Allows to build increasingly complex traps (higher levels ones need more expensive incredients) with each skill. Better ones have a higher chance to catch (=spawn as carcass in the trap inventory) more valuable animals within a given time frame (Say: Level 1 Trap: Bunny 5%, Beaver 2%, Mink 0.1%..., checked every n minutes). Setting the trap in certain locations increases chances (close to game trail: bunny +1%, close to water: beaver +3%...). Like the idea of lairs (bunny holes, beaver dams, ...) that are fixed objects like tree stumps. Setting a trap close to them should dramatically increase chances. I think a trap should start to work the moment the player is out of vision range (the animals avoid human presence). Raiding other people's traps is certainly possible. It was a major problem ín the real world.
Types of trappable animals:
we have:
bunny
beaver
we should have:
raccoon, wolverine, mink, ermine, marten, bobcat, lynx, muskrat, opossum, fox,
sable...