My son was using his purely for sleep too, but he started wanting it during the day, which was causing tanties so it went! lol
Around 24 months i put him in a Single bed, (was in Jrn bed) and simply told him that his dummy was in his other bed. He seemed to accept this ok (i think its important you are honest with her and explain what is happening. They take in more than you think, And be CONSISTENT with your story! lol).
I did have to sit with him the first 3 nights to get him to sleep as he wanted that comfort, but now he is really good and only wants the comfort when he is just in one of those sooky moods KWIM lol.
I think definitely tell your daughter something she will recognise, like you gave it to the garbo man, the postie, you lost, or maybe "drop" it in the garden and tell her its yucky now, it has to go in the bin. Does that make sense?
Just be repetitive! If you can get thru the first few nights, you will be fine! Just tell her what is going on!
Good luck with it!!