My DDs hair was too thick for baby shampoos starting at about 2.5.
We both have extremely sensitive skin (I get itchy if I even see a dryer sheet commercial on TV).
I use Free and Clear shampoo and conditioner for DD and it works really well. The conditioner really helps tame fly-aways, and the formula is gentle enough that she doesn't get itchy.
It's by the same makers of Vanicream.
https://www.amazon.com/gp/product/B00164E8TI/ref=oh_aui_search_asin_title?ie=UTF8&psc=1