Those might be little small to start hardening off right now. Most people wait until they are about 3-4" tall or taller. But if you are anxious to get them outside, then you could start now.
Regardless of when you start hardening them off, you need to start by putting them outside in temps above 50 degrees (60 is better). The first couple days, put them in shade for about two hours a day. Then increase the time and direct sun exposure a little more over the next two day, say an hour of direct sun and two hours of shade or under a tree where they will get a mix of both for the entire three hours. Then increase it to 4 hours a day for a couple days with 2 sun and 2 shade. Do this for about a week or so and they should be fine for permanent outside living. But since you live in growing zone 9b, you might want to give them a little more hardening off time as your heat might be a little too much too fast for them. Kind of keep an eye on how they are doing. If they are doing well after a week, then put them out. If they look a little stressed after a few hours in the sun, then you should continue the hardening off process. Also, keep in mind that sun is not the only factor in hardening off. Wind is another. Your plants are not used to dealing with wind and even a 10mph breeze would probably flatten them to start with. Make sure when you put them outside, they are well protected from wind and gradually increase their exposure to that as you increase exposure to the sun... Putting them inside an open cardboard box that is taller than the plants for the first several days works well.
Up here in Wisconsin, I usually rush my plants outside and have to worry more about frost than the sun so my hardening off process is shortened but my first year growing peppers, I did give them a good case of sun burn before I learned about hardening off.
Bruce