Yes. That's how you know you're ready. Look up impostor syndrome, sounds like you have it.one more question, is it a common thing when you receive a big responsibility to feel as if your not ready :'D
As far as continuing on in the restaurant remember that the chef left you in charge for a reason. If you're scared to branch out take little steps. How about continuing the status quo for a little while and getting some experience running the kitchen yourself before you start making big changes. Then you can be creative in the specials you introduce while leaving his menu intact for the time being. It's not big ideas that are going to move things along, it's the confidence you gain that will allow you to move forward.