Great question ....
Applying for another position within the same company may single everyone there that you are looking for a better job, period, and while you are applying within, you also may be applying elsewhere. And that may raise question about your long term loyalty.
But, if your experience there has so far been positive, you are already a family member and that can help you stand out above other applicants. If it's a quick fill position and/or early in the process, the combination could make you a shoe-in.
So ... mention your time there as a positive in a sensitive way and go for it.
Good luck!!