"Putting her out" may be not be GA - it may be sedation. They ended up putting an IV w/sedation "stuff" in it in my youngest since mine kept waking up five minutes after they would give her a dose orally. She had an MRI at 2 months old. You may need to push for it as most doctors seem to be of the wait and see mindset, though I see no advantage in waiting for the MRI.
In our case, I told a client of mine about my kiddo's situation - the client was a neurologist (unrelated to my work, I am in engineering). I was hesistant to do so, as this neurologist is a very nervous guy, but I knew that (since he is so nervous) he would insist she needed one. Once the pediatrician heard that a neurologist thought she needed one, we had the MRI within a few days.
Use all of your resources. Also, if you have a PPO (don't need a referral), just start making appointments within any in-network specialists that may help your cause.
She has also had GA twice at a surgery center, and was free to leave about an hour after waking.