Field Engineer and civilian engineer (ie, civil, mechanical or whatever) are two entirely different things. Our use of the word is as old, but very different. Field Engineers are also referred to as Combat Engineers, the second term is perhaps more descriptive.
Our officers hold some kind of Engineering degree, but it's still fairly peripheral. Engineers are required to know math and stuff, and physics is good for bridge building but it is still an entirly different trade.
As Patriot said, the only way you get an engineering degree through the Army is going to RMC. The actual soldiering stuff is done in the summer.
On becoming a Field Engineer Officer. First, a word about becoming an officer. It's really a good idea to be an NCO and a private first. That way you can learn about how the Army works from a Private's perspective before you start having to bear a lot of reponsibility. Especially if you are really young it's good to gain some maturity. For instance, I was thinking about being an officer but decided to do my basic first, I've now decided that I would like to have a lot more experince before I get a commision. (if I ever do) That said, to be an Engineering officer you need to be enrolled in, or a graduate of a university engineer program. (sometimes they accept Physics but not usually) You also have to pass the intellegence test, which is harder for officers, and pass a rigorious interview. The you go off an do you pre-phase and phase courses.
I did a reserve engineer course so it's quite a bit different. We have a six week course as opposed to a six month course, so it's really frantic and sleepless and physically really demanding. But here's my basic day.
We slept in tents and would wake up at quater to 5 in the morning and get ready for inspection. Physical training was at 5:30 with the course officer. Sometimes it would consist of running for half an hour (in formation, you have to keep up with the officer) or of log P.T. which involves carrying logs over your head and stuff. After P.T. was inspection, which consited of us getting yelled at and doing pushups and stuff. We did insane numbers of pushups. To go to the bathroom you had to do 50 pushups and 5 chinups. Eventually you don't even notice and start doing pushups for fun. We would march down to breakfast, have about 3 minutes to eat and then we would march off somewhere else. We were on the move all day, doing someting. Somtimes we'd get lessons in classrooms on explosives or whatever, but mostly we did hands on stuff. The lessons were pretty much spent trying to stay awake. (not that they were boring, just that we were really tired) Eventaully we would get back to the tent lines at arount 6 (most days) and then we would usually get in trouble for whatever we screwed up during the day. This involves extra inspections, show parade, whatnot. After you finally got out you would have a shower, study, and get ready for the next day. You'd end up getting to sleep around 11 or 12 PM. Plus you would have a 2 hour fire picket that night. So basicaly your days were spent in a sleep deprived haze. My QL3 course was definatly the hardest thing I've ever done in my life, no questions asked. You really earn your cap badge, but there is a huge feeling of accomplishment when you do. You feel like you can do anything now.
Reg force courses arn't generally as bad, you actually get off at reasonable times and maybe get some sleep. (although all soldiers learn the real meaning of tired)
WARNING: bridging is incredibly physically demanding. The bridge pieces are really heavy, and you end up lifting them all day. You are expected to life more than 100 pounds. Upper body strength is very very important to an Engineer.
Anyway, hope I helped.