For a pullet that is four and a half months old, she still looks like a baby chick, even discounting for the fluffed up feathers, which chickens do when they don't feel well.
I think what we may be dealing with here is a borderline failure-to-thrive chicken. These typically don't grow at the same rate as normal chicks, and they often never reach full size. In some extreme cases, they have the appearance of chicks long after they should have reached maturity.
The outward appearance isn't where the problems lie, though. Often these individuals have incompletely developed organs and digestive systems. One of their most common problems is that they can't seem to get warm enough, and that's because they don't process the calories they take in efficiently. They aren't able to generate enough body heat to get them through cold weather.
I believe you may have a "special needs" chicken. She will probably do all right as long as you keep her inside when it gets down below freezing. But she may have other issues stemming from under-developed organs. In other words, she's likely to have a truncated life span.
