Something bad could happen to you anywhere. Going to the corner store for a drink, going to work, the gym, etc. I've been traveling alone to foreign countries since I was a child. My parents would send me for the summer to my moms home country and since they had to work, I always traveled alone. A few years ago I did Ireland and England by myself. I've clocked many hours driving cross country for many years (until I got married and had kids) just for fun and never been harmed. I'll be doing a week long solo trip in September and people are more surprised that I'm doing *Disney* alone than traveling alone.
The potential for harm at Disney is always possible, as it is anywhere public. I don't imagine there will be many times where you're completely alone aside from your resort room. From your signature it seems you probably know the lay out of Disney pretty well. You know enough to do what any person (male or female) should do in a moment of danger. I'm definitely not old enough to be your mama, but if my daughter traveled alone, I'd want to know that she knows what steps to take if she felt in danger. Tell them that Disney has amazing security, both uniform and plain clothed. You're completely surrounded by cast members no matter where you look, etc.
These are all the things my mama heart would want to know. I'd still be a nervous wreck for my daughter to travel alone but that's a part of growing up