You probably CAN do it yourself, but if you're not familiar with the codes, I wouldn't. There are special codes that apply to bathroom outlets (need GFI, as you said), so either study up and do it ...
Based on the 2020 NEC. One thing I’ve learned from studying and following Code changes over the last 37 years is that the wording of a new rule is not always perfect. Sometimes it takes a few Code ...