When compiling Qt you can choose one of these options based on the configure command line:
no OpenSSL support (-no-openssl)
QtNetwork dynamically opening OpenSSL libs (-openssl; default)
QtNetwork linking to OpenSSL (-openssl-linked)
The last one means dynamic linking (if Qt is built as a shared library), or static linking (when doing a static build of Qt, i.e. -static).
So the ""solution"" to your problem is passing -static -openssl-linked to Qt's configure.
http://stackoverflow.com/questions/14566212/about-compiling-openssl-inside-qt-application