I have an 18 month old daughter and we stopped letting her use her pacifier?

She started biting her pacifier a few weeks ago which resulted to us buying her a new paci every 5 days..so we stopped giving it to her (as in in a very sudden way). she is now very grumpy and would wake up in the middle of the night looking for her paci..but we are firm not to let her use it anymore ever. now, my question is, how long will she be able to "let go" of her paci? will it have any effect on her development? thank you for your time to answer.