I personally think that a Quagmire spinoff would be awful. Quagmire is an OK character, but he's not a leading character. Not every character needs to be placed front and center.
A series built around Quagmire wouldn't work. First, it would have to be a very different Quagmire than the one we know on Family Guy; you couldn't just have every story where Glenn is horny as a hoot owl and chasing skirts all of the time.
Second, as previously stated, Quagmire rarely, if ever, learns from his past mistakes, so it would be hard to have moral lessons for him to learn.
Third, Quagmire is a bachelor. FOX would probably want to give him a family for the series, or worse, just stick Quagmire with a couple kids of making that he'd be forced to raise (Yuck!) in order to make the series more family friendly, which would completely work against his character (see reason #1).