We're thinking of switching to a different region at some point in the future. We're not sure when would be best with regards to our child's education and development needs? Would it be best to move when they're younger (kindergarden/grade school) and haven't had a chance to make a lot of friends, or when they're older and might be able to better rationally understand and cope with the move?
From my own experience moving 6 times as a child, and talking to others about their childhood moves, I would say the earlier you relocate, the better. Socially, in general other children are less accepting of outsiders the older they get. This is especially true if you're moving somewhere with a visibly different culture or accent. My wife moved from Texas to Arizona in middle school and still gets upset sometimes about the kids who made fun of her drawl.
Also, differences in educational standards and curricula are larger the further you are along in school, so the later you move, the less common foundation you have with the other children. For example, I was an A+ student in English literature, but unfortunately when I changed high schools my new classmates had all read an almost completely different selection of books. That wasn't a fatal problem, but made things more difficult because I didn't have that common frame of reference. My trigonometry is a little weak to this day because my high schools taught it in different orders.
I also find I have fewer childhood memories than my peers who never moved during childhood, and the ones I have are often more fuzzy. I attribute this to a lack of "anchors" to refresh my memory. For example, every time you drive by a park you remember events that took place there, but if you never drive past it in 10 years those memories get pushed aside.
I cannot offer research-based hard facts, but I can offer you my personal experience:
I've moved 16 times in my life, between 5 countries, at varying ages. (My father was a valued specialist at the time.) My bullet #2 would be most appropriate to you, but I'll list other ages for reference. In summary, I would recommend that you move sooner rather than later. Avoid moving kids at ages 5-15 when possible.
- Infant: No negative impact. My first move was local (10km), under age 1. I have no recollection whatsoever.
- Toddler: No negative impact. My second move was international, at age 3. I remember the old house and its surroundings surprisingly well, but I have no recollection of missing the place or any people there.
- Pre-schooler: Slight negative impact. My third move was international, at age 6. I had made some friends and just started school. Moving away caused some sadness, but the new place made up for it.
- Primary-schooler: Significant negative impact. My fourth move was international, at age 10. This is the worst time to move, in my opinion. Children at this age are developing their self-image and are very dependent on their surroundings. This move caused the biggest disruption and was not a smart thing to do, from my perspective then. The biggest problem was (not) being well received at the destination; children at that age can be very mean toward newcomers.
- Later: Significant negative impact. My fifth move was regional (100km), at age 15. I think that at this age, children have learned "who they are" and they're better able to cope with moving. They're also able to keep longer-distance friendships alive without frequent meetings, if they're important to them. Note: I didn't say it becomes easier! It doesn't. But older kids are more capable to handle the difficulties.
Of course, as already said, the earlier the better.
Later on, it would be wise to coordinate that with the moment that the child would change school anyway (like going from elementary to middle school, or from middle to high school).
I think it depends on the child.
Being the new kid is always hard, and there are a number of movies that depict this in detail (can't cite any now!)
However, inevitably, it all depends on the child and their ability to manage themselves socially. When I was in grade school, there were new kids that were extremely well received, and new kids that were just loners. It all depends on the child, how and sociable they are.
How social a child is has a dependence on their interest range, whether or not they can relate to kids in the new area. And that's way beyond the scope of this answer.