Covariance matrix after rotation

I encountered this question when developing a Kalman filter for a moving target using a camera on a drone. The problem is:

Assume I have a position measurement p1 with covariance matrix R1. And I have another rotation which is in the form of a quaternion q. This quaternion has a covariance matrix R2. Then what is the covariance matrix after I rotate p1 by q?

I have googled for a very long time but could only find the solution when q is a constant.