You are right, DropCap does not work in a header and it can't be pasted in.

A couple of options:
1 prepare it in the body of a document, do a screen shot, crop so you just have what you want in the header, and paste it into your header.
A second option would be to set up a table in your header with the first cell holding your initial cap. You would want to adjust the paragraph indents on the other columns so they would snug up next to the cap.

This (below) is an example of a DropCap screenshot cropped for pasting.


I suspect you would get sharper text with the table, though. If using a screenshot, the image should be saved as a vector image rather than jpg.