Thanks. You set me on the right track.
The problem was that I wasn't actually using the Qt MinGW package. I just thought I was. I was using a four year old version of MinGW I had installed in C:\MinGW since that was earlier in the PATH. Qt Creator seems to automatically add its MinGW to the beginning of the PATH so it was using the correct version of MinGW while I was using the old one.
So a pretty clear sign that cleaning up my PATH is well overdue. (Also in there, 4 year old GTK.)