Here's a few things to take into consideration when buying your dog pushchair or stroller.
Make sure the pet stroller has a good sized interior for the dog to sit down comfortably. If you are taking two dogs, this is even more important. There are dog strollers which can accommodate two dogs if you really need one.
Make sure the carrier can take the weight of the dog! I imagine people with massive dogs might not be catered for!
Check that your dog can see out clearly and that the stroller cover has a good-sized mesh window at both the front and the back. When it's raining and the cover is over, the dog will still like to see where s/he's going!
It's a good idea to get 'all terrain' wheels which can go up and down sidewalk kerbs as well as the gravelly, bumpy areas in the park. In fact, if you live in an urban area 'all terrain' wheels make the job much more effortless. The front wheel will benefit from being manouverable too, so that it can go round corners smoothly.
Some strollers have a little step-up on the front so that the dog can get into the stroller without too much effort. Some models have an entrance at the back of the stroller.
Other attributes aren't much different from a baby's pushchair - brakes, storage, quick folding, etc.