Since your using Queue<T> (recommended), Queue.Synchronized can't be used.
But besides that I would use the thread pool. But your EnqueueTask method kind of implies that the threading logic is handled outside of your "TaskQueue" class (your method implies that it is a Queue of tasks).
Your implementation also implies that it is not "Here" we wan't to add logic but rather in another place, the code you have there isn't really blocking for long so I would turn things upside down.
It also implies that the thing taking things off the queue is already on another thread since you use "PulseAll" to weak that thread up.
E.g.
public void StartQueueHandler()
{
new Thread(()=>StartWorker).Start();
}
private int[] Dequeue()
{
lock(_locker)
{
while(_taskQ.Count == 0) Monitor.Wait(_locker);
return _taskQ.Dequeue();
}
}
private void StartWorker(object obj)
{
while(_keepProcessing)
{
//Handle thread abort or have another "shot down" mechanism.
int[] work = Dequeue();
//If work should be done in parallel without results.
ThreadPool.QueueUserWorkItem(obj => DoWork(work));
//If work should be done sequential according to the queue.
DoWork(work);
}
}