The Royal Canal Way is a 91 mi trail that starts in Ballybough in Dublin City, Ireland and ends just outside Longford town near the bank of the River Shannon. The trail is an easy-going path that can be cycled, though it can be on a muddy bank at times. The trail is perfectly suitable for dogs, though you would want to confirm with your accommodation that it is okay. People do wild camp along the trail, but to find a secluded private space will be challenging. There is plenty of farmland near the trail, and many farms will likely facilitate you if you ask kindly in advance.
For resupplying you shouldn't have any problems. You will pass through plenty of towns, and passed plenty of restaurants for when your hiker hunger kicks in.
You can walk the Royal Canal Way pretty much any time of the year, with the best weather and temperatures being during the summery months of May to September.
WARNING: Some sections of the Royal Canal Way require a divert onto the road for a short period. The improvements were not finished at the time of writing in July of 2020.