What's this white dot above my baby's lip? It's been there for a month.

This sounds like 'Milia'. These are small white bumps on the baby's face. They look like whiteheads, but they are small cysts filled with sebum and keratin (a type of protein that makes up the outer layer of skin as well as a person's hair and nails). Sometimes Milia are present in the gums. They are very common during the first few days of life and go away eventually without any treatment.​ I don't think there's any need to worry - it should go away soon! Of course, if you're still concerned should it stay for much longer, check with your paed - they know best!