I am not sure about the Army, but for the AF, you cannot get on base housing unless it is considered a PCS. PCS's are 6 months or longer.
As an AF wife of a now retiree, I wouldn't go for multiple reasons.
1. Finding housing off base can be exhausting.
~ If you decide to go, look into
www.militarybyowner.com This site is great because they do rentals too. Plus, since they are military members that own the home, the houses are typically in an area that military members reside.
~~ IE at Elmendorf/Ft Rich, military members that rent or own jokingly call Eagle River the base housing of the North (North of the base/post) Your car breaks down and someone on your street or around the corner can take you to work. This was also true when we were at Bragg and Seymour Johnson. Many of these developments can have 30%+ that are military.
2. Imagine packing and repacking within 5 -6 months.
~ Think about it. Packing out will take at least 2 days. You may have to wait a couple of days to get your household goods delivered. Boxes and boxes of dishes, linens, clothes, etc. will be delivered. You probably have about 7K pounds to pack out and unpack. Look around your home. Start looking at taking down everything off the walls, and spackling the nail holes. Look in your fridge because unless you can move there door to door, all of that will be pitched because you can't take it with you. Depending on the mover, they may say you can't take any liquids, open dried good or spices too. That includes everything from shampoo/soap/olive oil to oregano to Captain Crunch cereal.
~~ Repeat 5 months later. That is a lot of work or money if you have to replace everything.
3. He will be very busy with BOLC.
~ If you live close to home, spend time with the family and make memories. You will be traveling the world soon enough.
4. Socialization.
~ Many spouses do not go because of points 1,2, and 3.
5. Do you work?
~ Finding a job for 5 or 6 months might be hard.
6. How old are your children?
~ School, pre-school age? They have friends and moving to them is upsetting. You move them for this TDY, and now they have to make new friends all over again. If they are young they bounce back, but they don't understand why within a yr they have to do it again. Keeping them in their schools with their friends makes it an easier transition in my opinion since it is only 1x instead of 2x. That and see number 2 where they want a certain toy or video while you are packing and unpacking...it could be 2-3 weeks in boxes during transit.
In the 20 yrs he served, I went twice for a 5 month or less assignment (TDY in AF terms), both times we had no kids. Once the kids were born, I never went. Reasons why are what I listed above, but the top ones were #4. Spouses didn't go because of #1-3. The 2nd was #6.
I hope this helps. In the end you need to do what is good for you, your marriage and your family. This was just my personal experience.