I'm a man, and I've been to Dubai.
I wouldn't tell a woman that she shouldn't go there.
Feel free to go there but take precautions.
It's not the place you go to if you want to party and get wasted.
So don't drink too much alcohol; or don't drink alcohol at all.
Don't go out alone at night, and steer clear of dangerous parts of the city, if there are any.
And maybe most importantly: Don't go there with a male friend you don't fully trust.
Dubai is very safe compared to other big cities in the world, and bad stuff can happen everywhere.
Why is it so safe?
I have some theories.
Many people do bad things when they are drunk or under the influence of drugs.
Alcohol is very restricted in Dubai, and it's not tolerated to be drunk in public.
The use of illegal drugs is probably not tolerated either.
Besides, I was told that 85 percent of the inhabitants of Dubai are foreign workers, and if they break any laws I guess they are kicked out of the country.
Therefore they are less likely to break their laws.
This link compares crime in Dubai and New York City: http://www.numbeo.com/crime/compare_cities.jsp?country1=United+States&country2=United+Arab+Emirates&city1=New+York%2C+NY&city2=Dubai