Passport for infant?

I’m due March 12 with my first child. It was an unplanned pregnancy, but I’m embracing it. Here’s my dilemma: I’m scheduled to visit England for ten days at the end of June with my mom. It was supposed to be this year, but we pushed it back a year because of the pandemic. We scheduled the trip as sort of a mother-daughter getaway after my step-dad’s passing, and it’s really important to her. I already know I’m not comfortable leaving my infant for ten days, especially since I plan on breastfeeding, but I’m curious how our passports will work out since there’s such a short amount of time to get everything in order. Has anyone here ever travelled out of their home country with an infant? I’m guessing I should order an expedited passport, but I also have no idea how traveling works with an infant. Any advice would be appreciated.