while (true)
{
BasicDeliverEventArgs e = (BasicDeliverEventArgs)Consumer.Queue.Dequeue();
IBasicProperties properties = e.BasicProperties;
byte[] body =
You're currently blocking on the Consumer.Queue.Dequeue(). If I understand your question correctly, you want to asynchronously consume messages.
The standard way of doing this would be to write your own IBasicConsumer (probably by subclassing DefaultBasicConsumer) and set it as the consumer for the channel.
The trouble with this is that you have to be very careful about what you do in IBasicConsumer.HandleBasicDelivery. If you use any synchronous AMQP methods, such as basic.publish, you'll get a dead-lock. If you do anything that takes a long time, you'll run into some other problems.
If you do need synchronous methods or long-running actions, what you're doing is about the right way to do it. Have a look at Subscription; it's an IBasicConsumer that consumes messages and puts them on a queue for you.
If you need any more help, a great place to ask is the rabbitmq-discuss mailing list.