I moved DS into a cot at about the same age. I was worried about it, but one day I just put him down in his cot for a day sleep - and he slept no problems whatsoever. He never went back in the bassinet! Not long after we moved him into his own room - again, I worried, but he adjusted just fine (me on the other hand spent the whole night worrying about him, lol).
More recently we moved DS (who is now 2 btw) from his cot to his bed. I was worried about this transition, but he was fine again.

I guess what I'm trying to say is, sometimes we're worrying over nothing!