It would be a bit unusual to have peri-oral dermatitis at that age. More common is a condition known as "lip-lickers dermatitis" that is caused by excess moisture from repeated licking of the lips.
I would recommend that you have your daughter's pediatrician take a look to see if she may need a mild steroid cream to help the rash resolve.
Advice and opinions given are based on the information provided and must not be considered an official medical recommendation. The limitations of the internet prevent an appropriate evaluation. Always consult your doctor if there is concern.