I used a daisy 880 to kill dozens and dozens (possibly over 100) of bunnies 6-7 years ago when I first got into air-gunning. The only thing I would say is, Know your limits well! Take the gun and shoot groups until you know what it's limits are. After a couple thousand pellets, I discovered that I could accuralely, consitently shoot a rabbit in the head at 25 yards, no further. the groups opened up after that where only a heart-lung shot was acceptable, and even that limited out at 35 yards.
I actually enjoyed hunting with the daisy 880, I had to crawl and stalk waaay more then I do now with my .22 cricket with 32 fpe.
Do not hesitate to hunt with it, it has plenty of power to do the job, and to do it well, just do your homework with it at the range before you shoot critters.