I didn't see this when you originally posted, I've been crazy busy with work so haven't had much time or energy for Node-RED.
It is almost certain that it will work with uibuilder as I designed it to work with any framework. I've not found one yet that it won't work with.
It is easy to have a go and wont take you long. Install the framework via a uibuilder node so that uibuilder starts serving up the library. Find the actual file(s) that you need to include in your own front-end code (index.html) and then rework the default uibuilder template code around the framework.
Actually, I've just looked at the home page and realised that I did look at Quasar when I was building v2 of uibuilder. At the time, bootstrap-vue seemed like a better fit because of its simplicity for getting started and I seem to remember that I had some problems getting Quasar to work - can't remember why now though.
It may also have been a reliance on using webpack which makes life complicated when you only want to do something simple. I can see now though that it seems to have improved its documentation.
You should be able to easily adapt the instructions on this page to work with uibuilder:
In fact, I'd recommend not installing it at all to begin with, use the CDN version as mentioned on that page. From the default uibuilder template index.html, simply strip out the bootstrap-vue references and put in the Quasar ones.