Let's outline few more of the problems. As others have said, Qt brings little to the party. Low latency audio is not something its multimedia framework is designed for.
Architecture:
Commercial soft-synths are invariably written as plug-ins for other audio software. The advantage of this approach is that the architecture of the plug-in is quite constrainted and somebody else has solved many of the hard threading and performance problems. Steinberg's VST and Apple's Audio Units being two obvious examples. Both are these are capable of tacking latencies in the order of milliseconds.
Real-time characteristics
When considering real-time systems, the worst-case-latency. In the case of audio, it's duration of the sample buffer in wall-time plus whatever overhead is required to accommodate the worst-case delay in getting scheduled by the operating system to perform and complete the processing.
Threading:
When writing a synthesis plug-in, you are really only concerned with two things:
- Implementing a render handler - which is called by the host when it needs samples generated by the synth, and which is generally called in a real-time (or at least elevated) thread priority.
- Implementing an event handler - which is called in a lower priority thread. The complication is that this should cannot cause a priority inversion in the render thread - with which it inevitably shares some data structures. You need lockless data structures for this.
Somewhere you must manage modulation of soft-synth parameters and parameter automation - possibly in another thread.
Naturally, plug-ins often also have UI, but this runs at the lowest priority on the UI thread, and should be totally decoupled from the render handler, via the event handler.
Host applications
If you insist on writing the host application as well, you would be wise to do what almost everyone else in the industry does, and use Steinberg's ASIO layer.
However, you might also checkout Juce - which amongst other things includes a plug-in host using ASIO, example plug-ins, and just about everything else you need to solve your problem.