Cycle touring with a dog and trailer

I'm planning a big tour around the UK with my dog this summer. Would love top tips on a suitable trailer that will be robust and light enough for us to do a combination of off road and small lane biking - and she's nosy so she needs to be able to see the world go by!

If anyone can help or has done anything similar I'd love to hear...

 

I've seen people on RABGRAI (a weeklong ride across iowa) using those two wheel trailors meant for their children. They zip up so the dog won't go running off, have mesh so he can see, and are stable. I don't think they are suited for anything narrow or offroad. I've seen dogs in bike baskets too, but they were really small dogs. I figure a one wheel trailor would probably be too unstable for a dog. You could always build a narrow two wheel trailer...