My daughter is 1 1/2?

I stopped giving her a pacifier before she was 6 months old and gave her a sippy cup instead of a bottle shortly before her first birthday...she now absolutely needs a sippy cup of milk to suck on to fall asleep...Am I insensitive to try to take this away as I did the others? Is she too old to still be needing this? Or would just making her quit with it cold turkey too much? It's just what leaks out of her mouth and drips on the linen begins to smell, and not only that I don't want her to keep this habit forever..