The hutch you have may be better quality, but I was given a small used hutch just like that, and my concerns with it are these: the construction is very poor- the materials used are very thin 1/8" plywood on the wooden portions, the wire floor is held in place by wooden guides that are not well secured, the tray is too shallow to allow for normal potty output which would quickly result in the dreaded "poop piles" in the corners, yet removing the tray would be unsafe because predators could easily push the wire rack up and out of the way. The nesting area does not have a "lip" at the bottom, and the kits could easily crawl out and freeze. Remember that a rabbit will not move her kits, so she will not take them back to the nest.
I currently have a VERY pregnant cat in mine, and it is inside the wire run of my "cat coop" so is better protected from predators. She will only be in there temporarily before moving into the cat coop itself a day or two after giving birth.
Personally, I would keep your doe in her wire cage as long as she is protected from windblown rain and snow. They are much more sanitary than wooden cages.