My 13 month old daughter has the beginning of tooth sprouting from her palate. What is happening?

Part of molar tooth. 13 months is the perfect time for the first dental visit. Baby teeth erupting from the palate is not common with baby teeth. Sometimes the back molars can look like they are erupting from the palate because you only see part of the tooth or cusp coming in first. A dentist can easily check this for you.
Tooth in Palate. If your 13 month old has a tooth erupting in the palate as you describe, that may present unwelcome problems. I suggest that you visit a pediatric dentist for a proper diagnosis. It may be possible to have an early orthodontic appliance inserted which may guide the tooth as it erupts.
Second molar erupts. This probably is a second molar eruption. There is no alarm though the tissue may be tender during the erupting process.