I walked a slightly longer version of this loop with my dog in November and the Pittencrieff park was still looking beautiful. Theres quite a few steps and hills, particularly when you go to and from the river path. The river path is the most beautiful part, with loads of squirrels on it. Past, that you walk into the town, passing next to the gorgeous abbey and then up the main streets. The second park I walked through, not in the official route is less interesting, but still a nice place to go through and is much less frequented so I could let the dog off the lead for a bit.
All in all a very nice, easy walk with plenty to look at and lots of smells for the dog.