It is a great idea to add a layer of mulch around your new tree. It adds much-needed nutrients to the soil, helps to keep the tree moist and keeps the grass from competing with the tree for nutrients. A good ring of mulch also helps to keep the lawnmower away from the trunk of the tree. Cuts on bark from a lawnmower can allow insects and disease to enter the tree.
Remember not to pile mulch high around the base of the tree. A layer of 2 to 3″ is plenty.