Cast swarm - when to expect brood

Hi

Andrew kindly provided me with a swarm in early November. He said it was probably a cast swarm, as it was small.

The colony is doing fine in terms of drawing comb, collecting pollen and nectar, but as yet no sign of brood (and I haven't spotted the queen yet, though I imagine she will be harder to distinguish before she starts laying in any case).

So I'm wondering whether I should be worried about the lack of brood yet, how long I should leave it before worrying about it, and if I don't see any brood after x number of weeks, is there anything I can do (eg obtaining a mated queen), to help the colony.

The colony is at the top of Belmont - not sure how many prospective drones there are within mating range.

Thanks in advance for any advice/suggestions

Chris