Don't go alone (commonsense for any Muslim country). But as far as Muslim countries go, it's one of the safest. I went there for my sisters wedding.
There are many Western women walking around without hassles. Just be aware of what is and isn't acceptable, as ignorance of this is what gets non-Muslims into trouble.
e.g. wear respectable clothes, don't let your boobs hang out etc, don't take photos of women, don't be affectionate towards a partner in public, and so on. These look bad in print, but really, it's not that bad at all. It's simply an act of observing the respectful things you need to do in another culture. You're ethnic too as I am, so you know what I mean.
I really became aware of just how Islamophobic we are in the West, much of it is unwarranted. Not all Muslims are psychos like we think they are. Many of them are just as normal as us non-Muslims (that aside, I still strongly disagree with the sexist nature of their culture, but in Dubai the women have more rights than in other Muslim countries).