You can check the thousands of similar threads, but in the end it is always an individual compilation/installation problem on the user side.
A short checklist:
1) Edit qwtconfig.pri
2) Build in release mode
3) Use make install ( no manual copying )
4) The designer plugin needs to be in a directory, that is read by the creator
5) The path to the Qwt dll needs be in the PATH variable
On Windows you have more traps ( debug/relase, dllimport/dllexport ) and no concept of a distribution at all. I will never understand, why it is common use ( don't know about you) to ignore the installation offered by the package and to prefer to copy files around manually.
Uwe
Bookmarks