What is a good starting dose of Prednisone for an average size Mouse having respiratory issues?

A mouse with respiratory issues wouldn't generally be given prednisone - this is an immune suppressant, which could make a viral or bacterial pneumonia worse. For Asthma-like conditions, bronchodilators are more likely to be given.

Prednisone functions like the hormone cortisol in the body, so the dose must be carefully calibrated to the individual animal - a generic dose for an "average sized mouse" isn't possible to determine.