Should I replace my queen?

I'm a new beekeeper in Alabama and was wondering if I'm jumping the gun. I installed my NUC a month ago. Did an inspection yesterday and 2 weeks ago. There was no visible change in comb development with one frame having no comb drawn at all. The brood seems sporadic but wasn't sure with a new hive and new frames if this was common. The Queen was active, but I did not see her laying during my inspection. Also, no queen cells were being developed.

Being that its a new hive should I replace or let the hive replace the queen?