Using DOSbox in a browser, two separate users on QL Forum have got a DOS-based QL emulator running in a browser window.
One has set up QPC1 (the older DOS version of the QPC emulator) in DOSbox to run a small collection of demo programs. Try this out at https://www.kilgus.net/qpc/live/
Another has set up QLay to run in the DOSbox, which in turn runs a ZX81 BASIC simulation. Try this one out at http://zxsimulator.orgfree.com/
I used Edge in Windows to display these – I have not tried other browsers.