If not, no - by itself it is an expansion and needs the full game and previous expansions on the account.
That said, I think there are bundle deals at the Blizzard store for the initial game and all the expansions.
If she doesn't have an account yet, it could be a great idea to look at the Recruit-A-Friend thing too :)
Edit: Ignore what I posted, they have started to allow gifting digital MoP so you should be fine.
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