Peat moss potting soil? Is that a mix of peat moss with other things? If it has other things such as fertilizer or anything else with chemicals/minerals I would transplant again...
Oh and the soil should be moist, and unless you placed the pot in a really deep dish of water I doubt you have it tOo wet. Just always keep the soil moist and never let it dry out. As BigCarnivourKid said, just leave the pot standing in 1/2" to 1" of water (distilled, RO, rain). O and if its an unglazed clay pot, it may not be good because it dries out a little faster than plastic pots, and also, the minerals from past uses or water will tend to stay in the clay, not good for carnivorous plants.