How to determine quantity of baking powder for baking simple cake?
For doubling a recipe, yes, you double the amount of baking powder.  Issues with increasing a recipe rarely cause trouble until you get to 4x or more.  

For baking though, you do want to make sure the depth of the cake is the same as for the original recipe though so that it bakes properly in about the same amount of time.  

This recipe from Bon Appetit is a sponge cake for a 13"x 9" pan or a 9" round cake pan.  It mentions that you can double it for a two-layer cake with no other adjustment for the baking powder.  

A common mistake may be to also double mixing time -- which you do not want to do since that can cause gluten development.