The answer to this question depends on the age and confidence of the child. We have life jackets in all sizes, and if you are used to kayaking, it is okay to paddle with a small child in your lap in a one-man kayak. It is also often possible to sit two adults and one child in a two-man kayak, with the child in the lap of the one sitting in the front. A child big enough to paddle a one-man kayak on their own can do so, accompanied by an adult.
Remember that all kayaking is at your own risk!