Most of the Ingles is either country tracks or tarmacked country roads. There are one or two parts where you walk along a single track at the edge of a field, especially on the stage to Betanzos. You may just need to pick up the buggy and baby for 100 metres or so. I would also avoid the 1 hour walk alongside the motorway on the way to Sigueiro, especially if your baby is sleeping at that hour, and because pushing the buggy on a grass embankment for an hour will be tough. Instead of turning right onto the grass verge when you go over the motorway bridge, carry on along the road, going straight over the next crossroads, and then simply following the road all the way to Sigueiro.
There are also two 20 minute tough climbs out of Pontedeume and Betanzos, both on tarmac. The way out of Pontedeume is especially steep to walk up, let alone push a buggy up. However, it is the start of the day, and there is a bench to rest halfway up
As
@biarritzdon rightly says, restaurants, cafes, shops and water fountains are few and far between on the Ingles. You may only pass 1 or 2 per day on some stages, and may walk 2 hours or so between one and the next. You therefore need to take enough provisions and sustinence for you and the baby, or the walk will become very testing.
this is especially true on the 2 days between Betanzos and Sigueiro, where there are basically no shops. I am assuming you are staying in private accommodation. As
@ElAines suggests, book up in advance, so as to be sure you have a room for the night