I have a small amount of Javascript to test, but it operates on the entire page, for example, finding elements by numbered ids like \"#t34\". I need to create a handful of
#qunit-fixture is automatically reset by QUnit, which means you can fill it with markup used by each test, or leave it empty and have each test fill it to leverage the auto rest. Or just use markup that you reset individually after each test.
You can refactor per-test setup and teardown using the module method: http://docs.jquery.com/QUnit/module
In this case it sounds like a good option would be using (synchronous) ajax requests for each test, loading the page markup you need into the #qunit-fixture element. That way you only need custom setup, as QUnit will reset afterwards.
Even if you're dealing just with local files from the filesystem, as long as they are in the same directory as your testsuite file, you should be able to load them via ajax.
If not, its easy enough to get a local server running, e.g. via "open http://localhost:8080/ && python -m SimpleHTTPServer 8080" in that directory.