Hi, Wendy! Welcome to the Orchid Board!
December to April is a normal time of year for these to bloom. Growers can get them to bloom at different times by controlling greenhouse temperatures once buds have set.
Most people repot orchids when new roots are forming. That will probably be soon after the flowers finish.
There is a lot of good information here on hybrids of D. nobile with other species. Most of this applies just as well to the species:
Edit June 15 2020:
Yamamoto Dendrobiums in Japan hybridizes and produces a great number of these plants. Their Web site formerly had excellent growing information for hobbyists. Unfortunately it is no longer there. You can still look at the varieties they grow, and maybe see one very similar to yours.
I saved the page, and summarized it in a post in this thread:
Uncertain if Dendrobium is still alive
Yamamoto now has a
page showing how to force Dendrobium nobile for Christmas flowering in Japan's climate. There is a lot to learn from that page, but it is intended for growers who can artificially heat and cool their greenhouses during off seasons. Note they use coconut husk for growing medium, which many orchidists would say retains too much water for orchids. For many orchids that is correct, but this is a very thirsty orchid.