I have done Dubai twice and I'm going back again towards the end of this year.
I absolutely love Dubai and not once have I felt unsafe.
Just remember to follow their laws! Cover up and just be careful around Ramadan when you can't eat in public during the day. Hotels are good though, they will still have food available for you but you won't be able to go out during the day.
I've seen girls walk around with denim shorts on and a lot of angry eyes followed them (including my own) until someone told them they had to go and change.
Have a great trip!!