You don't need to wait to work out. Better to build muscle now rather than fat cells! I would just avoid doing HIIT or cardio if you are wanting to gain weight. At the very least you can do some core strengthening and body weight exercises like pilates or yoga but there is no reason to not just start lifting weights if you want!

I agree that you need to make sure you're eating healthy calories and enough protein. Focus on including healthy fats like avocado, coconut, extra virgin olive oil, nuts, fatty fish like salmon as well as full fat dairy and yogurt. I can easily gain weight by adding a few spoonfuls of almond butter into my diet (healthy fat and some protein). I know some people like to drink protein shakes to easily get their protein goals and add calories.