in addition to a sot, as some have mentioned, i would suggest you consider a kayak with a large cockpit, such as a perception sundance or old town loon, or a tandem kayak.
i have the sundance 14 and the cockpit is roomy enough that my 4-year-old sits at the front end of the cockpit, not in my lap, and her position does not hinder my stroke at all.
a popular old town model is the dirigo. i’ve sat in it w/ my kid and that center “dashboard” hinders leg movement for the child. it makes it tough to slide the child’s legs in and out, which i think may pose a hazard in the event of a capsize. with the sundance, we both just pop out when we practiced self rescues.
the largest dirigo comes with a child jump seat that you have to buy separately. i think that forces the child to sit facing the stern, as in looking at you. i don’t know for sure, there wasn’t one to try it out.
if you should choose to go this route, know that the bigger cockpit means the boat will be wide, which means it’ll be strictly a rec. kayak. you won’t win any speed prize and you can’t do anything fancy with it, but on the other hand, it’s very stable and great for slow and calm conditions. i’ve taken my kid out on it many, many times and we both love it. it’s a trade off between a sleek kayak and time with my kid, and the kid wins, hands down. i’m going to buy the kid a fishing pole next and we’ll be doing some fishing.