Do you guys know any reliable source that would tell if Elmerf was a bunny lad or lass and how old was he/ she? Because that, I believe, influences on the behaviour of Legolas' dear pet - or should we call that bunny in this case a domestic animal...
Depending on the status of the hares of Mirkwood, they might have been considered as domestic animals.
Anyway, I think that Legolas would have preferred a male hare for the job of a Prince's personal domestic animal. For so lofty a job must even the youngest novice rabbit have unswerving fidelity and good looks (of course). Elmerf had to act like a noble ambassador in public, but who knows what he was busying himself with on his spare time