This depends on what you mean by “web application”. If you mean an application that can show parts of a web page in its interface as rendered HTML, like a browser can…yes. Qt incorporates something called QtWebKit:
http://doc.qt.io/qt-5/qtwebkit-index.html
(Note: Back in the olden days it was Microsoft–I think–who first made an embeddable Internet Explorer control so that you could fetch a URL into the midst of some MFC or VB application and run a browser in the midst of your otherwise-form-based application. The event hooks for Microsoft’s solution sucked, Qt’s are much better.)
Anyway, this is great if you want people to install your application on their machine, where it fetches web data but takes advantages of native features to be richer than a browser could. But be careful because these days native apps have to be really outstanding to surpass the advantage of something that runs in a browser they already have.
HOWEVER If you are trying to use QtCore to push server-side content out and fulfill web requests, that’ll be an uphill battle. You might find some related examples if you look hard enough:
https://web.archive.org/web/20100922075100/http://labs.qt.nokia.com/2006/12/20/whats-this-cgi/
Very few people use C++ (much less Qt) to generate web pages server-side. Yet there are still some doing it, even in pretty cool ways:
http://www.webtoolkit.eu/wt
…regardless, QtCreator will be no help in that kind of pursuit.