Gap of Dunloe

There are organized tours departing from Killarney that will take you across the lake, thence via one of the pony traps to Kate Kearney's, and then a return via bus or van to Killarney thus completing the loop.
If you choose to do it on your own then the traps depart from KK's and only go to the head of the Glen and back ... about 7 miles round trip. There will be uphill sections where the driver will ask that you get out and walk a bit to spare the horse. You'll have plenty of time for photos.
In late September the crowds will have dissipated and there's less urgency to get there early - still not a bad idea though.

We did this last summer and although we had a rented car, we took the tour that picked us up from our hotel just outside Killarney and then the jaunting cart from Kates, to Lord Brandon’s and then Ross castle. All drivers are a bit different, but we did wish ours went a bit slower. I should have been more forceful in requesting that we slow down. The crossing on the lake was slow and if not for the driver telling stories, it would have been boring.

We plan on doing this as well. Is there a website for booking the pony trek in advance? Or is it just done on site when you arrive at the location?

You can book the organized tours in advance from Killarney. If you choose to do it yourself from Kate Kearney's then I believe it's first come, first served - am not aware of a website to book ahead for that. All of the drivers seemed to be independent operators.
They start moving the jaunting cars from the stables near Lord Brandon's Cottage at around 8:30 AM in order to be in place at the other end of the Glen by 9:30 or 10 as I recall, so getting an early start during the height of the season would be a good idea. Probably less necessary in late September.