We moved to Germany when my dd was 20 months - her language was quite advanced for her age and she was bothered that other children didn't understand her (other children played happily with her, probably assuming her English was baby babble - she still looked quite babyish as she was little and round without much hair ;) ). She started to pick up the language quite quickly but didn't become truly bi-lingual till she started Kindergarten the month she turned 3. However she had lots of friends and spoke German perfectly well enough to play by then, and once she got going she seemed to relish learning new words and phrases (she did consciously notice the 2 languages - I remember her commenting "Little boy says Ente but it's duck!" - whereas my son, who was born here couldn't have told you which language he was speaking and seemed not to notice there were 2 languages going on around him, until he turned 4.
DD had been going to quite a few 2nd birthday parties for the children born to my antenatal class friends, most of whom she was used to seeing several times a week, in the weeks before we left and even though she was not quite 2 this had fixed firmly in her head the idea that she would also get a turn at having a birthday party, and she was very concerned about whether her friends would be able to come to her party - we told her it was a bit too far but she would have new friends to come to her party, and I made sure we did invite every child close in age to her in the village and have a big party (even though I was 9 months pregnant, and her brother was in fact born the next day, but it was important to her and I am so glad we did).
DD did miss her friends even though she was so little, but taking her to toddlers as soon as possible (I think the second week after the move) and spending loads of time in the village playground with her helped her make new ones, and then she was fine.
Somebody else commented on sleep issues though, and even though DD seemed mostly totally happy in the day her sleep did go totally to pot - she had been a bad sleeper as a baby, til about 9 months, but had been sleeping through for almost a year by the move, but once we moved she was hard to settle at bedtime and waking lots of times a night - I ended up sleeping on her floor unti her baby brother was born.
Some of it with DD could have been the fact the move and the birth of her little brother came close together - she understood about the pregnancy and actually she relaxed and her sleep improved once he was here, so she could have been anxious about what his arrival would mean, it is hard to separate what was the move and what was the imminent arrival of a new sibling.
We did talk to DD about the move in advance, she has grandparents here and that was what we focussed on, and the fact we would be going on an aeroplane and living next door to a playground (we had to drive to get to one in the UK), before the move she seemed happy and excited about it, and overall she settled well, but I think blithely assuming "kids are adaptable" is not necessarily the best way, as some are in their own little bubble at 2 where as long as Mummy (and maybe Daddy) are there it doesn't matter where they are, but others are very tuned into what is going on around them!