I've been on 3 cruises solo, as well as other travelling -- and it's been fine. Occasionally there's a feeling of noticing that most everyone else is with someone else or a group, but overall it's great. Ask to be seated for dining at a larger table, so you meet some folks, go to the singles gatherings, participate in activities, sign-up for a couple of shore excursions (or arrange some along the way with people you meet). It's just about the safest way to travel (or maybe even the safest). It's a lot more comfortable not having to share a cabin! I haven't gone on a
Disney cruise (yet) -- there will of course be lots more kids than on other lines. Just participate in lots of things, be outgoing, and have fun!
(I also once rented a car and drove around some of the Yucatan in Mexico -- to Chichen Itza, Uxmal, and Cancun -- by myself). Just do your planning, act like you know what you're doing and go for it!