I did the last 100 km in September with my four year old grandson and his father. Fortunately, the father was capable of carrying a 65 pound load on his shoulders! For the first three days, the boy walked about 70% of the time with his 5 pound pack (a good quality pack with the load being mostly the iPad and water bladder). Then the percentage began to decrease.
We found staying in albergues was too much of a burden on the other pilgrims, so we stayed in private accommodations after the first two days. Hotels were fully booked in many villages, so we had to adjust with taxi shuttles out and back to the Camino. It will be worse in June, July, and August.
There is little to interest a toddler, so the Camino became a search for the next children's playground. There are plenty. The daily pace is slowed by the playground stops, so plan accordingly. Your walk will be centered around your child, not yourself, other pilgrims, the Camino, the food, the history, or the religion.
For a three year old, a stroller is probably a good idea. Our backup plan was to buy one if necessary. There are stretches where a stroller will have a hard time going, so it should be a durable one, and you will need to be capable of pushing it while carrying your own pack.
About all that my grandson remembers of Spain is that "they speak Spanish there," but he had a good time while he was there. My son and I loved it, but then we were able to share the burden of taking a child. I think you should contemplate what is in it for you, what is in it for the toddler, and the real reasons you want to do it. It is absolutely certain that it won't be an experience like most the one for most pilgrims!!! If it is your first camino, you will want to mentally prepare for the stress of a new experience for both yourself and the child. It will be demanding both physically and mentally. You can train for the physical, but the mental will depend upon your personal resources. Whatever negative happens to you, it will be doubly negative for the child...
