My son has a tufted angioma on his leg. When he was 2 days old, they tried an MRI but it didn't work, so they did one the next day on anesthesia. He ended up having to stay in the NICU for one night, because his temperature dropped from the anesthesia.
However, he's had anesthesia 7 times since then (he is 20 mos now), once for a biopsy, more MRI's, broviac tube insertion, etc and he has had no other problems with anesthesia. He didn't even require a hospital stay overnight (except for when he was already admitted).
I'm not a doctor, but I would push for the MRI, even though she'd need the anesthesia.