I did a tiny change at the QT DemoBrowser example and added a line to change the useragent at webview constructor.

this->page()->profile()->setHttpUserAgent("Test");

If i execute the js code

navigator.userAgent

on the console at all tabs i get the result "Test".

If i execute the js code

window.open("https://www.w3schools.com", "_blank", "toolbar=yes,scrollbars=yes,resizable=yes,top=500,left=500,width=400,height=400");

on the console at e.g. the first tab i get a new window.

If i execute the js code

navigator.userAgent

on the new window i get

"Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) QtWebEngine/5.9.1 Chrome/56.0.2924.122 Safari/537.36"

I expected "Test". If you have a different Qt WebEngine Browser running it can also take there useragents