Not egg, no. If I'm correct, it can only be a Pokemon, and you send it to your Black/White game via the Poketransfer lab in Route 15. That lab is only accessable once you have defeated the Elite 4 + Ghetsis & N. If your Eevee is a Pokemon, not an egg, you can give it to your friend via Poketransfer, who than can give it to your White game