Currently their is no browser support for QC files, at the time when such support existed, it was limited by reasons of framework and plugin distribution base to Safari and any other WebKit plugin capable, OS X installed browser. See
the WebKit Plugin page for further details on exploiting Quartz Composer compositions within Safari [WebKit plugin browsers].
This current lack of cross platform, cross browser support for Quartz Composer compositions really matters little as such on the only platform currently supporting such compositions, namely OS X Tiger and Leopard.
For those of us wanting to to originate and program our own compositions, plugins and patches we only have to install the standard Developer's Tool package and open up Quartz Composer. For those wishing to only be consumers and users of Quartz Compositions, most will work in QuickTime Player unless specifically protocolised to only work as visualizers, screensavers and such. In that case, they will work as expected in their native environment.
Some compositions will depend upon the installation of 3rd party plugins.Redistribution of such plugins as a part of an installation package for the composition is entirely dependent upon the terms of the authors of that plugin. Thus far, this author has not found any plugin that can't be scripted upon its inputs, or be used to obtain data to be incorporated into some other from of compositional routine. A by no means exhaustive list of QC plugins can be found upon this site's resources page