I have had two solo business-y trips and three solo vacations to WDW so far, with another booked for January.
Was it weird? Well, maybe for about the first ten minutes, but then once I relaxed it was HEAVEN. One of the things I like best about going alone is how much less planning I need to do that when I'm with the family. The restaurants are fairly good about working in a solo diner with either a short-notice reservation, or no reservation at all, so I don't really plan any dining in advance when I'm alone. I do; however, book special recreation and tours in advance. I have taken backstage tours during solo trips. This is a great opportunity because most only allow guests over age 16, so the kids can't go anyway, and several tours include a meal, so you're can chat with other guests then.
What I really cherish on a solo trip is that I get to do exactly what I want to do. I've read whole novels sitting by the pool, gotten a haircut at the Grand Floridian salon, exercised, watched chick flicks on the DVD player in my room, gone on the rides that the kids don't like, gone on the same ride five times in a row that I do like, rented a SeaRaycer, lingered in the shops in Epcot's Future World, slept past 7:00 a.m. You get the idea ... you can be as busy or as relaxed as you want because it's YOUR trip.
You can read some of my other tips about solo travel in the posts
HERE,
HERE, and
HERE.
I can't say enough great things about WDW as a solo travel destination. I hope you get the chance to try it.