If you have something that small, I'd recommend a portable or rolling island which you can find from many locations. Try John Boos, Williams-Sonoma, and Sur La Table for starters. In most jurisdictions, a stationary island that exceeds something like 12" x 12" requires an electrical outlet hardwired to it. Also, if it's a small kitchen, you'll enjoy the freedom a rolling island will give you. John Boos in particular does some beautiful butcher-block top tables that can be used for direct food prep. Places like Kitchen Source and Butcher Block Co will be retailers for John Boos products.

I've been looking and cannot find a small, portable island with several drawers. That is why I wondered if wheels could not be added to a base cabinet to use. I really need drawers.

In our last house, 26 years ago we made an island to match the cabinets. The wheels were so hidden that when the new people moved in, they had no idea it moved, for years! The answer is yes. Check out thecabinetjoint for help. It's RTA so virtually anything can be done.

How about this? It is 26" wide when the drop leafs are down, has a tray/shelf and then 2 drawers. If the tray/shelf could function as a drawer that might help.

https://www.target.com/p/bristol-double-drop-leaf-kitchen-cart-white-crosley/-/A-77573387

I have an Ikea island card with two drawers and two shelves. I love it!

https://www.ikea.com/us/en/p/foerhoeja-kitchen-cart-birch-80035920/

I painted the base of mine black so it would disappear and used mineral oil on the top. Three years later, it still looks terrific!. I love that the drawers open from both sides.