Downloaded qt-everywhere-src-5.10.1.tar.xz, built(not easy, takes a long time) and installed. Sqlite is now working, looks like the Yacto supplied qt is incomplete.
Also a platform linuxfb is now available and working.
I just searched from google, you need to check if current bsp has this driver firstly, try to refer to the qt forum, I searched a link, hope helpful for you