Babies wake up at night. A lot. And it usually goes on for quite some time. Expecting a 12 week old to sleep through the night is pretty ambitious and...unrealistic. And just so you won't be too disappointed later on...let me tell you that there will always be SOMETHING to wake up your child. It's not like they learn to sleep all night in infancy and that's it, you're home free. Later on there will be teething, bedwetting, nightmares, obsessive searching for toys, needing drinks, needing the potty, etc... It goes on and on. How about expecting a 12 YEAR old to sleep through the night? That's more likely.
If the paci wakings become more frequent and you feel they are getting out of control, just stop giving it. You'll probably have to listen to her cry for a few minutes, but she should get used to it quickly.
Also, you might want to read "Healthy Sleep Habits, Happy Child" by Marc Weissbluth. This book explains normal sleep patterns as children grow up, so you know what to expect, what is normal, and how to fix problems. It's not a child-rearing philosophy or a force-your-baby-into-your-schedule book. It's just the scientific reality of baby sleep.