The switch you've to access is the static property DynamicQueryEngine.Switch.
If you do:
DynamicQueryEngine.Switch.Level = TraceLevel.Verbose;
you've set the trace level manually to 4. Though this indeed requires you to reference the DQE in your own project.
I know the line that creates the switch (the cctor in DynamicQueryEngine) is
DynamicQueryEngine.Switch = new TraceSwitch("SqlServerDQE", "Tracer for SqlServer Dynamic Query Engine");
but the field is actually inherited from DynamicQueryEngineBase.
Ironically I can access DynamicQueryEngineBase without an additional reference but it gets scrubbed by the above line on first use of DynamicQueryEngine.
Cheers
Simon
PS Is it just me but now I'm running IE7, I can't add smileys or formatting within text - each time I apply it, it puts the smiley/sections at the end of the text.