Based on my experiences in Prague (not as a woman travelling alone but merely as a fairly observant man), I think you'll be safe, especially if you stick to the well-worn tourist trails.

The biggest danger, which is unrelated to your sex, is undoubtedly petty crime, particularly pick-pocketing. It is rife, it seems, so be careful in crowded places, including on trains and buses. Divide up your money and take two credit cards, carrying them in different places. That way if something is stolen, you haven't lost everything. Keep a copy of the details page of your passport separate from the passport itself, too.

I can attest to the extortionate nature of some Prague taxi drivers. On the worst occasion a driver tried to charge a truly extortionate sum for a short trip back to our hotel across the river. Fortunately, there were three of us, and one of our number went into the hotel reception, whereupon someone from the hotel came out and after a few obviously well-chosen words the fare was reduced to something reasonable. I'm not sure what you can do about this except to try to negotiate the fare beforehand and/or to try to insist that the meter be turned on. We probably should have got the restaurant where we had been to book the taxi, rather than hailing it ourselves.

I have never had a problem with taxis to or from the airport, however.

The other thing you might encounter is marauding groups of youngish men from western Europe (notably the UK) on stag weekends. Although unpleasant, I doubt that they will seriously target someone in the street, especially in busy areas.