Lets ask nanobyte, he's a genius at languages and he's been studying french for 5 years. lol.....
btw, its j'ai eu un lapin... you can't say "j'eu"
and as claire said, they are both correct... to explain the difference is rather difficult!!! but they are not exactly the same, but i'll try anyway...
when you use "j'ai eu", you should generally say when. "qaund", so basically specify a time!!!. where as the other one, j'avais, its not necesary to state a time!!
hope that helps... ask your teacher for the exact reason why they are different!! If you don't have teacher, check out the difference between passe compose and Imparfait..