I have a collection of rabbit feet given to me by cats. When you sleep near a tamed cat, it will jump into bed with you and usually leaves you a "gift", which is often a rabbit's foot. Of course, this is not the best way to collect rabbit feet, but I thought it was worth mentioning.
Not sure if it's too late, but: I obtained several rabbit feet by putting a sword with Looting III on it in my off hand and sniping rabbit's with a bow in the desert. No matter which seed or map I was on, there were always multitudes of rabbits in the deserts and you can easily snipe them from a distance, so they won't try to flee.
IF you have carrots this makes catching rabbits all the easier, but if you don't have any carrots yet it's really not that hard to chase after a couple and leash them. Just bring along a fencepost so that when you leash the first one you can keep it tied down while busy with the second.
You may find it helpful to just randomly go chasing after rabbits without actually trying to catch them just to get used to the way they hop around. After a bit of practice, you can start anticipating which way they'll go and this will effectively slow down the rabbit enough that you can get some better clicks in with the leash instead of clicking wildly (protip: don't just spam-click the leash as you might accidentally unleash the rabbit you finally managed to leash). All in all, it's basically the same thing one does in 1.8 PVP so if you were familiar with that system then rabbit-catching should be no problem.
In my experience, chasing the rabbits can be problematic, as they sometimes leap randomly and can jump off a high area to their deaths as i have observed. The ones in the desert are also prone to jumping into cactus when excited, not seen one jump into a lava pool yet ... there is a couple of lava pools in the desert near me, maybe i'll give a go
It's best to do it in a relatively flat region, yes, and you may want to prep the area first (ie, remove all the cactus, cover up cave holes, flatten hills/fill in depressions, etc) just to minimize the jumping around that can cause you to fall back into walking mode. Especially in a desert where only rabbits (and therefore lots of rabbits) will spawn, they won't really be going anywhere. As I said earlier, you may want to just spend some time randomly chasing rabbits so that you can watch how they'll react over extended periods of running-away and this same tactic can help you improve your jump timing so that you stay in sprinting mode for longer (this is key because the rabbits will be moving faster).
Also, from my attempts, the rabbit movement when chasing after them doesn't appear to be all that random...I think it's just a matter of the fast pace in combination with the small hitbox and the flee-when-too-close mechanic that makes it seem more random. Having speed effects going may also throw off your timing, but that might just be a "me" thing as I typically don't have magical effects present. I definitely am noticing a much-improved ability to leash wild rabbits relatively quickly.