Are these two applications going to be run on the same machine? Is it going to be Unix only system?
If yes, you can take a look at named pipes, FIFOs, Unix domain sockets and shared memory. On windows named pipes and shared memory are available too, but I'm not sure about the rest. You can also consider DBUS (there should be windows port, but I'm sure if windows version of Qt supports it).
Which one to use depends on the protocol you want to use to exchange data. There won't be any problems with GPL, if you are going to have two separate applications that just exchange the data.
Edit: Personally I would consider Unix domain sockets and DBUS (esp. if you can use Qt for the driver as well).
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