I wouldn't let my dc have a dummy at this age. We went cold turkey with dd just before she turned 3. She wanted hers constantly, though she was perfectly happy to go without for the full day at nursery, the minute she came out to the cloakroom she was rummaging for her dummy. It was just habit but clearly fine without.
So we decided to do away with it. I had been putting it off for ages, dreading the fuss and drama, but she got over it really quickly, say 3 days. And surprisingly, we stayed with sill v shortly after, and dn is addicted to his dummy (usually has 2 clipped to him and one in hand) and they were lying all over the floor etc and not once did she reach for one or say she missed hers or anything.
Actually I agree to a certain extent with snippy. It is babyish and unnecessary. I wouldn't want my dc to be sucking thumb or similar at this age. Is the dummy in all night? I can't believe it is in no way detrimental.
Mind you, what we did, following research on MN, I cut down the side seams of the dummies so they were broken and didn't give her the satisfaction. She complained a bit about them being broken, but still soldiered on, then a couple of days later I just chucked them out and that was that.
Sounds a bit like a power battle now to me, so the posters saying pick your battles - well, maybe it is a battle worth fighting?
For you to decide. But like I said my dd was a hardened 24/7 (at home) dummy addict and she went cold turkey without too much drama.