Not necessarily. In Belgium the King (and eventually queen) is the commander and chief of the armed forces. So it makes sense that Elisabeth is encouraged to at least do the one year program.
In the Netherlands, the monarch hasn't been commander in chief since 1983. So there wouldn't be the same pressure for a monarch to have experience. That doesn't rule out her joining.
I don't know. Is there an option in the Netherlands like Elisabeth is doing? Could she go in for a training program but not actually join the armed forces? Elisabeth is not enlisted, she is simply taking an one year program at the military academy. Is there such an option in the Netherlands?
I don't believe, correct me if I am wrong, that either of the king's brothers did military training. I know he did before he went to university.
I think they will likely wait until spring to make any choices. It seems to have been said earlier that the plan was for Amalia to take a gap year and then go to university. I would thin university plans would need to be cemented in the spring. If it looks like a gap year is not possible next fall, or may not be possible, she may just apply to start university right away.
If she misses her gap year maybe she will get the opportunity for a semester abroad program. Or some other chance to live abroad later on. Both of her Uncles did part of their university abroad. And she certainly wouldn't be the first heir to go to university in another country (Fred spent time at Harvard, Victoria at Yale, Felipe did Georgetown with Pavlos, Haakon at the London school of economics, Philippe at Oxford and Stanford). Her father did his university in the Netherlands but he had the chance to study abroad during secondary school having attended the same school in Wales that Elisabeth just graduated from. Charles and Andrew both spent time during secondary school abroad, Charles in Australia and Andrew Canada.
I assume she will likely take similar courses to many of the heirs have done. Political science, international relations type route. Her sisters will have more freedom in what they study.