Hello,
First - let me say - I think it is great you are trying to go even though you have a baby. I have seen many people try to discourage families with small children - but if you do your research there is no reason why you can't do this! I wouldn't have been brave enough to do this type of journey when my children were small - but now I wish I had done more with them (My last baby just turned 18). I did see 1 family with a small baby and a mother with a boy who appeared to be about 4 on my Camino.
If hiking on the
Camino Frances - you will come across towns frequently and all the towns or very nearby towns will have all the essentials of living - grocery stores with baby supplies are all over. That said - I think your biggest challenge will be to time your trips to the smaller markets. I kept going through towns when the smaller markets were closed. It drove me crazy. So - my recommendation is to have enough formula and diapers for 4-5 days at a time. Each time you get to a bigger town - resupply in those bigger towns. If you do that, you will be fine. Or - just get 4-5 days supplies each time you pass a market that IS open. It would help if you have a jogging stroller (by itself or in addition to a baby carrying backpack) because then you could store the extra formula/diapers etc in the jogging stroller and not carry on your backs. I say jogging stroller - because if bringing a stroller - you really need the bicycle size tires to get through the various terrains. There will be some places that are more challenging with any stroller though - so be aware.
I personally don't recommend mailing packages - as I found the post offices are always closed when I pass through towns. I don't know - my timing for small grocery stores and post offices is always terrible. That said - you could also do luggage transport between your starting/stopping points.
Also - consider where you plan to stay. Are you planning on private rooms? Because fear of a crying baby seems to be the biggest complaint I see when I see people tell young families they shouldn't do something like this. Wouldn't bother me (as long as it wasn't all night every night) - but there are many who might tell you not to do a Camino for that reason. They may have additional reasons for thinking you shouldn't do a Camino with your baby - but again - do your research and plan according to your babies needs and you (and the baby) will be fine!