@g.hirsch
I'm not sure, but you can change port number 1883 to something else and check again. It's possible on some systems this port to be in use.
By the way, first error means this:

The requested socket operation is not supported by the local operating system (e.g., lack of IPv6 support).

On a side note, the getter should be const, it doesn't modify anything in the class instance.

Hi and welcome to devnet,

Qt has not a module for that that you can clone from here. You can build it as any other Qt module: qmake && make && make install.

IIRC, background services with Qt are part of 5.7