Neither she nor you knows what that means, apparently.

Fixed gear bikes (and singlespeed, obviously) only have one speed. That bike has multiple gears and a derailleur, which means that it is neither. A fixed gear bike is different from a singlespeed bike in one way: a fixed gear cannot coast.

If you are just looking for a commuter, I would recommend a cheap singlespeed bike or a used bike of any kind, provided it is intact and rideable.