Planning to breastfeed and pump

Just wondering if it is possible to breastfeed exclusively at first and then add pumping in later? Can I pump one breast while feeding off the other so that I don’t have to feed and then pump afterwards? I will be traveling with my baby very soon after she is born and will need to feed/pump in public places so I’m trying to figure out how to make that work. I plan to be able to take my baby with me and be able to breastfeed directly pretty much 100% of the time but want the opportunity to store up some additional breast milk too for those times I need to be able to have someone else feed her.