Your daughter needs to continue her close relationship with you while developing other age-appropriate relationships. You may need to create opportunities for her to be with her classmates (one or two at a time) so that she can enhance her social skills.
Walking or driving your daughter to school is not bad, but try to expand her peer interaction by taking along a neighbor or picking up one of her classmates. You'll enjoy watching the two of them together, acting their age. Kids need to be silly and spontaneous sometimes - not acting like little adults.
Never being alone in the house is fine, as long as that doesn't mean you are always taking care of everything. Your daughter should have household responsibilities and should be required to do them.
Continue to show your love for her and enjoyment in being together, but don't use the relationship to keep either of you from establishing the important relationships that go with each of your new stages of life. Enjoy the closeness, but don't remain wrapped around each other so much. Hope these suggestions bring you new experiences and opportunities for growth.