error says qtquick2plugin.dll could not be found but Qt5Quick.dll was missing

While trying to deploy a QtQuick2 application I got the following error:

qrc:/Main.qml:1 plugin cannot be loaded for module "QtQuick": Cannot load library G:/proj/qwash-64-GL/QtQuick.2/qtquick2plugin.dll: The specified module could not be found.

It was frustrating because the qtquick2plugin.dll was present at the current location. It turned out the real problem was that I was missing the Qt5Quick.dll file but there was no error about this in my log.

My .pro file also included this line:
QT += qml quick widgets sql network xml svg

I expect Qt to warn about a missing dll such as Qt5Quick.dll and to properly signal the missing dlls it needs.