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It's difficult to say if this is a problem, since you have only had her for a short time.
It is possible that she has done this behavior all along.
If we knew that this was a new behavior, I would be concerned about the possibility of a structural change or growth in her throat.
The way to investigate this would be to have her evaluated by your local vet. I would start with a physical exam and sedation to examine her larynx/pharynx area.
If there is something abnormal seen, I recommend biopsy.
If everything appears normal, I would simply continue to monitor her activity level, appetite, and litter box habits.