I'm looking for some advice/opinions/notes!

I think Sadie would respond well to the CIO method, and I'm wondering when/how we should start implementing (she will be four months on Wednesday). She already goes to sleep on her own for both naps and nighttime sleep. She will usually just rub her hands together or rub her face until she falls asleep... sometimes she talks herself to sleep. Our issue is the recent nighttime wake ups, which I think are caused by a combo of the transition to the crib & a sleep regression. I know that she has the ability to fall asleep on her own, but now in the middle of the night she won't. She doesn't need the paci to fall asleep--she usually throws it out of the crib before she even falls asleep--but in the middle of the night, she cries until I go in there, replace the paci, and shush/sing/rub... half the time she won't stop crying until I rock her.

Last night she went to bed at 8:30, and was up at 3:00, 3:30, 5:00, and 6:00. She got up for the day at 8:00.

Basically, I want to know if y'all think 4 months is too early & how y'all think I should implement CIO since she is already able to put herself to sleep to begin with. How long should I let her cry before going in there? And, if shushing/rubbing doesn't calm her, am I supposed to pick her up? Any suggestions for calming without rocking?

As a quick note: she's FF & hasn't needed a night feeding since she was a few weeks old.