If it is the only google account on the phone the only way to remove it is a factory data reset/wipe.
Or you can get her to set up her own google account and once done you can remove your now superfluous one.

 

There should be a factory reset option in the SD & Storage Menu. That will wipe the phone completely (although stuff on the SD Card will be safe) and she'll be prompted to run through the setup process again. She'll lose her progress though, is she ok with that?

 

Kinda, but it's all tied in to licenses for purchased apps etc. You buy an app from the market and it's tied to the gmail account you bought it with.

I don't want to take this too off topic, but aren't you in a similar situation with your iTunes account?

 

Interesting. So If I create an iTunes account, buy some apps, my mates signs out of his on his iPhone, I sign in to his iPhone with my account, install the apps I've bought, then sign out, he'll have access to the apps I've paid for?

Forgive me if I've interpreted that incorrectly, I'm still a little tender from yesterday.

 

In Settings > Accounts & sync > manage accounts,
if you click on an account, you will get the option "Remove account" if you have another Google account setup on your phone. I have done it once.
I wonder why you din't get this option on your phone.

 

Hmm.. Wierd. Cant tell what app we install affects the functionality of the Android OS. It is too complicated