I think だいじょうぶです is understandable, but it sounds a little unnatural because it is usually used when you are asked if something bad has happened, or after someone bad has happened. Japanese people usually say "おかげさまで", "おかげさまで、元気です" and so on to answer "ご機嫌いかがですか". Both "いかが" and "どう" mean "how" in questions, but I don't know if they are completely changeable in any cases. The first is a polite expression, and the second is used in casual conversations as well.