A sprinkler needs at least 20 psi minimum to do what it is supposed to do. It will sprinkle with less pressure but it will be more like a dribble.
The very smallest jet pump will do what you need. For as little as you have, go to HD and get the smallest jet pump you can get, in plastic. If your "tea" includes fertilizer it will destroy any metal that you might get.
Life doesn't matter because you are going to use so little water. I would flush the pump with clear water after distributing the "tea".