I used to let dd fuss for a few minutes, and if she got to actual crying I'd go in and find it for her. I would not wait until she got really fully awake, just light real crying. Until she was old enough to have more mobility and could fend for herself a little, I would get it any time she needed it.
Once she got that little bit older (maybe 5-6 months?) she would wake up and want to party if I went in, so I started leaving her to self-soothe as much as possible, only going in if she got real heavy crying. Since she was probably 7 months old I rarely go into her room at night for any reason. And from what I can tell, now she uses the paci to fall asleep, it falls out, and when she wakes up she picks it up and sticks it back in, but is not sleeping with it in her mouth all night. And then we take it out of her mouth and leave it in the crib so it's for sleep time only -- I don't think we'll have any real problems with breaking her of the paci.
Your dd is young; I'd keep getting it for her (after a few minutes) until she gets big enough to start using her hands more or can fumble around and find it for herself.