Getting by on rabbit snares is definitely possible though you'll want to set up near good spots like trapper's cabin or jackrabbit island. The basic idea is pretty straightforward, find some reclaimed wood and cure those guts indoors for about 5 days, then you can craft a bunch of snares. You'll probably want 6-10 of them spread around since each rabbit only gives you around 560 calories when cooked well.

Make sure you've got a knife handy and a good fire spot nearby cause you'll be doing this daily. Something worth keeping in mind is that unlike throwing rocks, snares don't actually make the rabbits disappear forever which is pretty nice. The tricky part is managing your time since you'll need to check those traps every day, and carrying around raw rabbit meat tends to attract unwanted attention from predators.

A good setup would be picking somewhere like mountaineer's hut, placing your snares, then using the downtime to gather wood or craft while they do their thing. Getting your cooking skill maxed out really helps since you won't have to worry about food poisoning from older meat. Might be interesting to know you can actually break down ruined snares to fix others, so you won't run out of materials.

Just keep in mind you'll need quite a few rabbits each day to keep going, and you won't get those nice calorie bonuses you'd get from bigger game. Most folks use this as a backup plan rather than the main food source, but hey it works if you're careful about it.