As an outsider, it's obvious why she's waking - her whole life, she has slept next to you, she probably woke this frequently before, but heard/felt/smelt you and went straight back to sleep.
So ... you could try putting something in her cot that smells of you (the T-shirt you wore that day, for example). I got one of those soft toys that you could microwave to warm up, then you put it in the cot - they stay warm for a couple of hours, that may comfort her.
White noise maybe? Bet her room is a lot quieter now than she is used to.
If you think congestion is the problem, you could always slightly raise the end of the cot, but if you never did this in the bedside cot, seems a bit of a coincidence.
We put DS into his own room at 4 months, I was lucky, he slept better in there than with me, turns out I was keeping him awake! But the transfer from basket to cot was a little trickier, tried the above. Took a few nights, but we got there :)
Good luck :)