You can do more than that.
When you go to get your eevee, save before you pick it up. When you do, check its gender. if its male, turn of the game and repeat until you have a female. Now, when you unlock the sevii islands, island 4 has a daycare centre where you can breed pokemon. If you give the daycare lady your female eevee and another male pokemon which can breed with it, the egg produced will be another eevee. If you have taught the male pokemon any TM's, this new eevee will have the one most recently taught. Then you can evolve the new eevee into whatever, with some funky new moves!