The Qt configure script has the following options:
-openssl ........... Enable run-time OpenSSL support.
-openssl-linked .... Enabled linked OpenSSL support.
What is the difference b/w the two options?
run-rime: Qt application will need ssleay32.dll, libeay32.dll (if on Windows) to run (place it near executable, or it may find it in system32 directory, again, if we are speaking of Windows).
linked: Qt application will contain all needed OpenSSL code inside executable, so no external .dll/.so needed.
On Linux, it might be more "natural" to use system-wide (run-time) installed libraries, as OpenSSL will be most probably installed, and automatically updated when security fixes are made.
On Windows however, it might look more convenient to link statically, though distributing few dll's more is not quite a big difference (since using Qt you will need bunch of them). There might be some issues finding proper OpenSSL compile/link options to link it successfully though (in my quite old experience), but you can try.