I put Liam in his own room in the cot when he was 7 weeks old, I originally was going to put him straight in his room in the bassinet, but I had a ceasar and it made it easier at night time or when he woke I could be there quicker in our room as his room is down the other end of the house.
I started by everytime he got dressed or had his nappy changed it was done in his room so he could get used to it. Then he had a few sleeps during the day in his cot (not very good ones though, but we were also having sleeping issues at the time).
We decided to try him in the cot (expecting a bad night) after leaving him one night with my parents and he slept fine out of our room so we just went for it and had no problems, in fact he slept better in the cot as the mattress was firmer.

We bought a monitor so we can hear him and you'd be surprised how easily I wake up when he cries yet to no other noise, not even hubby's alarm. I am a heavy sleeper to so I thought I wouldn't hear him but if you hear bubby in your room, with a monitor you'll still hear Hannah in her own room.
Tommee Tippee make one that has a nightlight in it, which I've found very useful plus it has a volume nob that you can adjust as you get used to the noise. I now only have mine on the lowest setting and find it loud enough.
You can only try it if she's not into it you can always bring her back to your room. Ladies at my mother group still have their babies in with them at 4 months, so don't feel you have to rush it.