We moved when our daughter was 15 months old and it was quite heart breaking

even though it wasn't far away, just a couple of miles.
Every morning when she woke up there were more boxes around the flat. Obviously, she noticed that something was going to happen and when I think of the day when we actually moved (friends and family helped us), she was so different! Well, I felt really sorry for her and I do think that they notice the change and I wouldn't be surprised if they were a little scared too, because the little ones really don't understand what's happening.
Anyway, maybe I was just too sad about the move
In generel, I really think it's fine to move with a little one. They will learn and understand with time but as with everything in life, they have to learn that changes are normal.