Boy this might get me in trouble. This whole business of labs that do everything from fetching ducks to overhauling a big block Chevy was started years ago by an outdoor writer that took his lab,,,,you guessed it, rabbit hunting! He related how great his supercharged lab was on rabbits. I'm sure a lab would wotk on rabbits and I'm also sure anyone of a number of other breeds and non-breeds would also. None will probally be as effective as a Beagle!
Seeing as you've already got the lab and can only have one dog, you answer your own question, train it! But I reccommend James Spencers book on retrievers. I had Wolters book on pointer's and was turned off to the point that I threw the book away; I wouldn't even give that book to any one. With pointers his methods are,,,,,questionable at best. You don't scare the hell out of a dog to teach it "whoa". I've no reason to believe his retriever book is any better. There are a number of books I've heard of on retrievers you might also check. What evre you do, get several different books and pick one that fits your temperment or, if you have a temper, pick one that teaches YOU to control it.
Good luck!