I was asked privately about this, but I don't feel like giving a detailed response for one person at a time so I'll post more here. Having some experience with forums on related subjects such as soapmaking, I'm trying to anticipate questions and resolve them. It's a FAQ, but not a frequently answered one.
What's so hard about making baby shampoo or baby wash? First we have to ask what "making" means. When hobbyists refer to making soap, they usually mean doing a chemical synthesis, involving a chemical reaction that changes the starting materials into what is sometimes referred to as another molecular entity. However, some hobbyists will also refer to simply molding soap (i.e. changing its shape, usually via a melt-&-pour kit) as "making" soap; it was already soap, but you made it into a cake or whatever. Other people might exclude a mere change of shape, but consider the making of a mixture of ingredients (without any subsequent chemical rxn) to be making a product, the way we might make salad dressing.
Next I have to ask what makes a baby wash or a baby shampoo a baby wash or shampoo. I think to most people it's the unusual property (compared to soap or similar products) of not stinging eyes. Otherwise washing a baby is just like washing an adult, unless you have something else in mind differentiating baby from adult cleaning products.
No-eye-sting shampoo consists of a mixture of surfactants which are detergent (which is just a synonym for "cleaning") but, in combination, don't sting eyes at the concentrations usually used. To do that, the mixtures are of surfactants which are all less irritating in combination than soap (often the combinations are less irritating than most of the individual ingredients, for reasons unknown) and in addition include certain surfactants which, in sufficient proportion, prevent eye sting by other surfactants. The anti-sting surfactants are all nonionic surfactants produced by ethoxylation of certain synthetic glycolipids and/or monoglycerides. These are different from, but share some similarity with, the anesthetic surfactants that are ethoxylated alcohols or alkylphenols. The anti-eye-sting surfactants are not without controversy.
All of these surfactants are considerably harder to synthesize than are soaps; or, to put it another way, soaps are by far the easiest surfactants to synthesize from readily available materials, which is why soapmaking was discovered centuries before the other surfactants were. I don't know of any DIYers who are making baby shampoo style surfactants in that "making" sense.
That leaves the possibility of making baby shampoo by simply mixing ingredients, which is the way even most commercial makers of baby shampoo do it. (They buy surfactants synthesized by others.) Yes, you can do that. You can look at the labels on commercial baby products and get those ingredients. However, it's hard to get the ingredients in quantities small enough to be suitable to DIY.
On top of that, I'd expect most readers here, if they wanted to make their own baby wash or baby shampoo, to want it to be in some way different from the commercial kind. Usually they want it to be "natural", which AFAICT is really a synonym for old fashioned. Sorry, but baby shampoo is by its nature high tech stuff, a product of the last half century, at least if you go by the no-eye-sting criterion. As I wrote above, if you have some other criterion in mind, then maybe we can work on it. Or who knows, maybe one of you can discover something new that takes the eye sting out of soap.