No doubt in my mind you should do something to build some time before going to an airline. I don't even know where to begin with reasons.

Get your CFI/II/MEI and spend some time using them. You are in a good position, flight schools are desperate for instructors, as the regionals have sucked them dry. The school I left is now offering a few dollars an hour more than I was making when I left less than a year ago. You will probably be able to find an instructing job that pays more than a first year regional. Do it until you get bored, and then keep going for a few more months. You will learn a lot in the process, and be much more confident going into that interview, and into training.