Is QtQuick commercial? No GPL version?

IANAL but if you're making commercial products you need pay for QT. You can use GPL etc if you're doing open source I assume.

Qt has both commercial and LGPL licenses. I think you can develop commercial applications with LGPL and not distributing the source code of your own app, but you can't statically link to Qt's libraries. https://www.qt.io/qt-licensing-terms/

IIRC some of the newer libraries are being licensed under GPL (unless you pay for a commercial license of course)

That's not correct. You can use the LGPL version of Qt to develop commercial product without paying for a license and while keeping your source proprietary. You aren't allowed to statically link Qt under LGPL, but that isn't a big deal.

Does the LGPL deal with the fact that you actually pull in a lot of Qt code in the form in header files into your actual compiled binary?

Yes, my understanding is that including headers is not a problem for LGPL. If it was, LGPL libraries would be useless.

Note that the LGPL version of Qt doesn't contain everything the commercial version does. But there isn't a lot missing.