Yes, this is a know problem of Quake Live. It would be easily fixed if the Quake Live developers had a look at it, but they seem not to bother.
Actually, Quake Live is completely compatible with Firefox 4.0.1, and even Firefox 5.0. The fact is that the install script is broken, and want Firefox 3.x or lower.
You can have a look at this page to install Quake Live in Firefox 4.0.1:
http://www.quakelive.com/forum/showthre ... xes-insideYou just have to extract an XML file from the installer, edit two or three strings, and archive it again. Everything is explained on the forum topic I linked.