Hi,
I did a lot of touring with my old dog before he died and it was great. He was a collie dog which was perfect for the running and the training side. I adapted my old Bob trailer in the following ways:
I extended the carrying space over its rear wheel using the mud guard stays as support.
I cable tied the foam pipe insulation over the metal work where the dogs head rested (around the front of the trailer)
He was very well trained (easy with a collie!) and responded to commands for which side of the bike to run, and of course up!
He loved the trailer and sometimes if I stopped at a junction he would jump into the trailer on his own!
My son (not even a teenager for many trips) took a reasonable amount of weight and I also had panniers on my bike.
Big issues were the dogs fitness and sore pads.
nowadays you can get dog booties! which i would highly recommend. we made do with old socks and gaffa tape.
We off road cycle tour and had some great adventures in wales, scotland, orkneys, and the north and south downs. + lots more other little local trips!
we met some interesting people cos of the dog, but found it difficult if you did want to stay on a campsite. We mainly wild camped anyway, but be prepared.
some other things to remember:
Get a tent with a porch - no muddy feet then inside!
Dog food - get dried food which is designed for active dogs (I carried about 5 days worth at a time but it was often difficult to replace it with high calorie types!)
I wish he was still alive, he was great company on the trips and I would highly recommend taking a dog in the uk. Rabies jabs need to be done I think 3 or 6 months before departure - check with your vet.
oh yes I also clipped him to a medium length haired dog and I waterproofed a dog coat for him as trying to warm up a wet cold dog is not much fun for him or you!
Have fun, we did!