Well a few seconds after I finished the quest and turned it in I noticed this:

Umm well hi there? >> Why are you staring at me like that?

Oh great there are two of you now. And why are you still following me? You're creepy.

Go awayyyyyy! T_T You're not Buddy, you aren't as cute as he is!

FREEDOOOOOOOM! THANK YOU BATTLEGROUNDS!
....Or so I thought. She was actually right there waiting for me when I came back. And continued to follow me until I fled to Dalaran via hearth. I wonder if she would have actually followed me there as well....