Usually they hire from PE background but then again a lot of things can happen so it doesn't hurt to try. To be a drilling engineer you need to know about reservoir pressure (as it affects the drilling operations), the required mud content (oil based mud/water based mud ... where to use these type of mud) and probably some completion knowledge (fracking, acidization etc etc). I am not a drilling engineer but a lot of my friends are so I get to know what they do. I'm not sure if there are any members here who are a drilling engineer, maybe they can answer some of your questions.