Welcome to the DIS, Jessica!
I can't really say whether or not you should go to Disney with the person you described, but I can help with some of your other questions.
I have taken a few solo trips to Disney World, and I have to say that I really enjoy it. In all my trips to Disney World over the years, I have always felt safe while on Disney property with the exception of one incident (which I will get to in a minute). I keep my guard up when walking alone in the evening in areas that may seem a bit dark and not well travelled--just as I would anywhere else, but overall, I feel that Disney is a very safe place.
The one incident happened one evening at Jellyrolls when some guy was hitting on me. He was making lewd comments and gestures, and asking me inappropriate questions. He left my side three times and came back to sit with me even though the bar was empty and he could have sat anywhere. I was going to slip out of the bar at one point when he walked away, but he came back over when he saw me reach for my bag. He creeped me out enough that I approached one of the piano players I have gotten to know at the bar, and he was kind enough to walk me out of the bar in a torrential rain storm to catch a cab. If a situation like that arises, I know that I could also go to any bouncer, or contact Disney security to escort me to my room, cab, or car.
As for dining alone, that is something that is an individual preference. I have gotten used to dining alone because I travel frequently for business, and also travel to visit friends solo. So, I'm used to it. At Disney, I try to get a table near the window near a window so I can people watch while I eat. Or I'll study a guide map while I eat so that I can decide where to head next. One thing that I noticed when dining alone is that there are often other solo diners--especially in the restaurants at the resorts.
If you are uncertain about how you'll feel about having a sitdown meal alone, why don't you do a test run this weekend. Go to your favorite restaurant in your hometown, and see how you enjoy it.
You could also look into meeting up with other DISers. Look on the solo threads on this board to see if anyone is going when you are going to be there. Post a thread on the dining thread, or the meet board. I've made some wonderful friends on the DIS who I have met at Disney on more than one occassion!
As for Jellyrolls, I have spent many a night there by myself. I've been there so many times in the past year and a half that one of the piano players thought I was a local. Another one gets thrown off if I'm not sitting on my regular bar stool when I'm there by myself. So, don't worry about going by yourself! You'll have a blast! And if you see Scotty and Ray, tell them Karen from Boston sent you (it may get your request played faster). You can check out the schedule for the piano players at
www.thepianomen.com .
You could also try to organize a meet at Jellyrolls or Pleasure Island as well. Sometimes you can meet up with just a few DISers and have a lot of fun.
When are you thinking of going? Where are you thinking of staying?
Have fun planning!
Karen