They order it for you, you can't order it for yourself. You will go to their docs.
The earliest most can take the exam is in July. Last I knew you had to be deemed a candidate and since that usually doesn't occur until late June/early July you can't expect to get the DoDMERB request for many more months.
A DoDMERB medical exam will be ordered when your SA application is about half completed. I beleive for USMA, your essay needs to be completed. For xROTC it is requested after you are awarded a scholarship.
As stated don't sweat this - you have a long way to go on nomination process and the rest of the application requirements before worrying about DoDMERB.
DS got his nomination in Nov and didn't do DoDMERB until Thanksgiving timeframe senior year.
Having said that once the link comes thru do not waste any time getting the exam; remedials and waivers take extra time if needed and you don't find out overnight.