The only Qt app I've used recently is VirtualBox, which is terrible on the Mac. The controls don't look or work right at all. On Windows, it's less bad, but still noticeably non-native.
I searched the web and found that Google Earth Pro also uses Qt, so I downloaded that. It looks awful, too. The scrollbars, split panes, buttons, and toolbars look wrong. Checkboxes are drawn mangled, animation is absent, and the outline view doesn't size its rows correctly so the bottom half of text is cut off. Despite language being "System default" in the Earth prefs, and English being the top language in my System Prefs, part of the UI is in Japanese (my #2). The view right after launch: https://i.imgur.com/eDvSoUm.png
I think a good first step would be looking at existing Qt apps. Are you OK with the quality of apps like VirtualBox and Earth? Alternatively, do you think you can do a better job at this than Google and Oracle?
I think if you're planning to write a typical Qt app, in order to make 'native app' fans happy, you're going to be in for a surprise.