The area is practically in the historic center. Which in its self does not insure safety but I would walk around that area with no problems on my own at night. I am fairly independent and have never had a problem walking around Florence, I travel quite a bit and have had to catch the train and bus at scarey early morning hours and have always felt safe in the city center of Florence.
Of course, please remember safety precautions are the same where ever you go - so be aware of your surroundings, don't flaunt your wallet and bags and when possible don't roam the streets alone if you are unsure of where you are or where you want to go, especially in the evenings and nights....but then these are good rules to follow where ever you go.
That is the historical center - via Guelfa has a lot of shops and foot traffic at all times of the day given its closeness to the Mercato Centrale, there are a lot of smaller side streets I would avoid on my own at night. I would keep to the better lit streets (as you would anywhere else in the world) if I was alone and always be aware of surroundings. While there are incidents of petty theft/robbery/pickpocketing, I would never say I've ever felt Florence to be dangerous - and I've walked the center at night and alone and always seen people out and about on the main streets so have felt safe.