I have no idea where you are from but I'd make a bet you'll be safer in Dubai than in your home town.
I'm female and visited alone several times before coming to Dubai to live. I've never felt unsafe or uncomfortable here at all.
Dubai has a very low crime rate and there are no particular difficulties for lone women. There's lots to do and as long as you are happy in your own company you'll have a great time.
You can get lots of info from the Top Questions about Dubai on the right side of the screen on the Dubai forum (you've posted this on the UAE forum, you'll get more replies if you post on the Dubai forum). You can also search for recent threads on this subject.
If you have any specific questions please come back and ask.