Not touring really, but lots of 30 to 60 mile one day rides. Be patient, don't try to rush the dog too much, let him get out when needed. For a dog, especially a small one, be mindfull of the heat and when you are riding in the sun, small mammals (including small kids) ,do not have as much surface area as an adult human to get rid of the heat. Throw on a layer or two of fur and it's like riding with a heavy sweater. I carry extra water to wet down my small dog. I also let him go swimming, and then start to ride when he is still a little damp on a hot day. A trailer or basket must have flow through ventilation, from front to back. Try not to totally block his air flow.
Bring something like paper towels for cleaning up if he is sick onto your bike or trailer.