We are doing the same routine since my son was 13 months old (he is now 20 months old). It works pretty well. As you will see, we only give milk once a day, before going to bed at night. He never warmed to the idea of having milk during the daytime meals and I never saw any harm in giving him the milk at night - assuming that you brush the teeth afterwards and put him awake to bed, obviously.
I also have to say that I leave him to cry for at least 10min at bedtime before going in again. That said, he usually doesn't cry because he knows that we take bedtime very seriously and that there is no way that he is allowed to play. When introducing the routine, I was very strict about it - I'm getting a bit softer now... smile
5:30am Wake up (unfortunately he only needs 10h30min sleep). But I leave him in his cot for another 30min.
6:00am Night light switches on, he is allowed out of bed. Weetbix for Breakfast.
9:30 Morning Tea
12:00 Nap (he sleeps 1h20min or 2h)
2:30 Afternoon Tea
4:30 Snack (he gets really hungry in the afternoon)
7:00 Sippy cup of milk, teeth brushing, one lullaby song, BED!!!
(If he wakes at night, I wait at least 10min before offering some water and a cuddle. Usually he goes back to sleep by himself - I get up every 10 days or so).