Regardless of whether they fly year round, much of brood production is based on 1)programmed instinct from the past million years. 2) The shortening or lengthening of the days. 3) Whether there is a flow.
I would imagine that for most places, without stimulation from nectar and pollen being brought in, brood production slows or stops. Many commercial places in California or Florida must stimulate feeding to get brood raised in winter, even in warm climate areas.
The only way you will know about the queen is to do complete inspection and find the queen. There are telltale signs of queenlessness, but are hard to see if you have not seen it before. There will be a distinctive humming coming from the hive, etc.
At this point, until the third week of December, I would not expect to see brood production. ;)