I’d say it’s part of growing up, and a healthy feeling. I’m living on my own now, truly alone in my house for the first time since I left home at 18 (I’m 27 now, but I always had roommates). It’s a wonderful feeling to look after yourself. You will feel lonely, though. I have two cats. They help me sleep better, because I know I’m not alone in the house. If I hear strange noises and the cats don’t react, I can be sure that it’s not someone breaking in!
On the other hand, if you’re looking forward to being on your own so there’s no one looking over your shoulder as you drink, smoke, and party until the early hours of the morning, you’re probably not ready yet!
I must say, my relationship with my parents has become much more loving since I moved out. When I’m looking after myself, I can respect my parents much more for all the effort they put into looking after not only themselves, but four children as well.
Good luck in your new place!