Small rocket stove in a Tiny House on wheels

Hi Permies!

My husband and I are looking into building a tiny house on wheels and are wondering if it's possible/practical/safe to build a rocket stove into a mostly wooden home with no concrete floors. We are considering a raised design to keep excess heat from scorching our floors and building in a small bench for thermal mass. The area we would have to work with would be an area of about 1 1/2' D x 3' H x 4' L. The height measurement is for the bench overall height, not the heat riser. Also, would it be safe to build a simple J style rocket stove for indoor cooking in such a small space? Possibly with a ventilation hood just in case? Any advice, experience, or guidance appreciated!