Welcome, Soaping Mama!
This is just me, but I personally would not use any soap at all on an infant. Most pediatricians I've talked to recommend using only water to wash a baby's skin until a child is at least 3 to 6 months old, especially if they have sensitive skin. Their skin's acid/alkaline mantle is still very immature in infanthood and has a harder time than adult skin in bouncing back from the pH changes that soap causes to it.
Having said that, to answer your question about oats and honey in liquid soap....I would add honey (mixed with a little water first to dilute) either to your cooled off lye water, or stickblended into your oils before mixing in the lye water. Don't add it at dilution time when all the lye has already been reacted, since honey is a food for bacterial growth in liquid soap if added when diluting the finished soap paste with water. If you add it at dilution after the lye has already turned everything into soap, the potential for bacterial growth is great unless you add a preservative. Although honey is a great preservative in and of itself to keep itself free from ickies, it is unfortunately not strong enough to preserve water-based products such as liquid soaps made with it.
As for oats.....I'm personally skittish to add oats to my liquid soap because it is a food, and foods carry the potential of bacterial growth in products like liquid soap unless you use a preservative, but also because they'll just fall out of suspension to the bottom of the bottle. Oats are better served in a solid bar of soap if you ask me .
IrishLass