If you batch convert (i.e., select several QuarkXPress files at one time to convert), you may see several fonts highlighted in pink and flagged as missing. If you convert each file individually you may not see this issue. The issue appears to happen because Q2ID creates files so quickly that InDesign needs some time to catch up with the on-screen display.
In this case, try placing a text cursor in the pink highlighted area and see if the font name shown by InDesign is what you are expecting. If it is, then save the file and re-open it in InDesign. This usually clears away the pink highlight.
If you place the text cursor in the pink highlighted area and the font name is not what you are expecting (it is usually enclosed in square brackets), then the font is missing and you will need to replace it with another font.