Are you sure she actually HAS a fever? A baby's temperature isn't a steady 98.6 like an adult's, they can't regulate their body temperature that well until they're toddlers. A baby's normal temperature can vary from 97 to 100.3. That's normal. Most pedis, including mine, consider 100.4 and higher a fever. You said her temp was 101, was that rectally? B/c the ear thermometer isn't particular accurate on squirmy newborns in my experience.
Yeah, how often has it been over 100.4? My pediatrician seems to have a pretty hard line that 100.3 is not a fever. It's normal as a first time mom to worry about all of these things, but it's also your doctor's job to talk you off the ledge and not get stressed about things that are not problems.
Fevers were an anxiety point for me, too with a newborn.
I assume you're taking her temp rectally (our Pedi requires that reading for gauging a temp). I think a lot of fluctuation is normal, per PP, under that 100.4 mark. My DS runs hot - still kind of does. I'd also find that I needed to give him a little time to regulate after a nap or something when he'd wake up all snuggled and warm. Often if I "thought" he had a temp, if I just let him cool off some it wasn't an issue.
A low-grade fever could also indicate teething - 4-mos is possible, though on the earlier side. If you feel that you aren't being listened to (our nurses line stresses that I should NEVER feel bad/silly about calling), then I think it's reasonable to consider another Pedi. I don't think it would be the strangest question they got if you wanted to at least talk to the nurses and get their opinion.