((((hugs)))) I do agree with PP if she is sleeping well at night, she's obviously not doing too badly - but, it is very little for a 5.5month old and I'm worrying that the overtiredness is going to build up and cause more problems.
At 5.5 months the average awake time is about 2hrs - 2hrs15mins. That is after a good night or a long nap. So after her morning nap (which is short), could you put her down much sooner for her next nap? So if she wakes at 9.45am, do another nap at 11.30am? I know it sounds really early but if she sleeps til 1, she should still be ready to take another cat nap on the school run?
What do you think, worth a try?