Yes you are allowed to do so.
Qt Designer is available under not just GPL but "GPLv3 with The Qt Company GPL Exception 1.0"
Here is the exception:
The Qt Company GPL Exception 1.0
As a special exception you may create a larger work which contains the
output of this application and distribute that work under terms of
your choice, so long as the work is not otherwise derived from or
based on this application and so long as the work does not in itself
generate output that contains the output from this application in its
original or modified form.
As a special exception, you have permission to combine this
application with Plugins licensed under the terms of your choice, to
produce an executable, and to copy and distribute the resulting
executable under the terms of your choice. However, the executable
must be accompanied by a prominent notice offering all users of the
executable the entire source code to this application, excluding the
source code of the independent modules, but including any changes you
have made to this application, under the terms of this license.
Exception no.1 fully covers your question.
Here's the repository for Qt tools https://github.com/qt/qttools.
There you can find the source code for Qt tools (including Qt Designer) and its licenses.