Is your MTB a hard-tail or full suspension? It's easy to put a rear rack on a hard-tail (heel strike could be a problem, however) and carry what you might need for 3-4 days without the added complexity and weight of a trailer. I have no experience with disc brake systems, so that could be a problem - your LBS may be able to help there. A rack system for a full-suspension bike may be cheaper and lighter than a trailer (other than purchasing a used child trailer from a yard sale or Craigslist).

In addition to searching the forums, what kind of roads and trails do you expect to ride? A single-wheel trailer may be your only option depending on trail conditions. For example, the C&O Canal Towpath - it is mostly very flat packed dirt & gravel double-track, so you'd expect it to be very trailer-friendly. There are sections where the tracks are separated by a wide grassy hump that would cause problems for a 2-wheel trailer. At the other extreme, my neighbor rode the TransAmerica route pulling a Burley Nomad (2-wheel cargo trailer); one of his travelling partners pulled a single wheel trailer. Both riders were pleased with their choices. As for transporting a dog, you may want an enclosed trailer (either designed for carrying an animal, or re-purpose a child trailer. Most of those are 2-wheelers (I've seen a few very pricey single wheel dog trailers).