It's not late to start thinking about that; it's the perfect time. If you haven't yet, I would suggest looking for some navy/military forums and asking for advice on how you can use your degree within the Navy. I'm sure there are opportunities but I don't know what they are and being in the military you'll have to be prepared to be put where they want you and not necessarily where you want to go.
I do remember I was flown out to Huntsville's Redstone Arsenal to meet the crew as I was selected for a position there in early 2010. Aside from the government testing areas, there were large buildings for Boeing, etc. If I remember correctly, they would usually have some military engineers about the place although I don't know what they did. I never got to learn because about 1 month later Boeing was shorted on a contract which caused a lot of fuss at the arsenal which lead to the direct loss of numerous jobs which included mine. Them's the breaks.
I was never in the military myself but my dad was for 22 years. I'm sure you will do your homework but I can't stress enough that you need to know what you want, and how to get them to give it to you, before you sign up. Of course it includes things like bonuses, benefits, etc. but it also includes things like promotion paths, etc. Look far in the future. Do you want to be a fighter pilot? Commander? Test pilot? Astronaut? Etc. They all have best ways to get there; look them up. It will be hard because like 99% of people you're thinking and dreaming nothing but flying, "Just get me in a plane and I don't care!". Lots of things you have to ask for, specifically, and often nobody will ever tell you those things exists nor will they tell you how to get them. Be prepared.
That includes preparing for what you want to do after you retire or leave the military. Lots of positions aren't bound for glory but will net you big bucks when you leave; know what they are so you can plan on getting them now. The best example I can think of is flying the OH-58 in the Army. Everyone seems to focus on the Apache, Blackhawk, etc. Ask around, though: no OH-58 has to look for work long after they leave with decades of OH-58 experience. The main reason? The OH-58, unlike most other military helicopters, is not overpowered. They need a bit more finesse on the collective and throttle and get much more time at low altitude maneuverability. Ask an OH-58 pilot how blackhawk pilots fly, for example, and they'll say they try to jerk the collective right off. No finesse
Re: Andy, I remember watching Neil deGrasse Tyson talking about when he was a kid and seeing a list of all the people in congress and what their professions were. He couldn't help but exclaim, "Where are the scientists? Where are the engineers?". Pity.
I looked and found it!