I moved DS1 at 2.5, which was fine. I was a single parent and nobody had an opinion, so I just waited until it was more annoying to have him in the bed than to not. Since he could walk and I put him straight in a single bed I did about 2 nights of going back and forth and then cried on MN about it and someone said "Why don't you get him to come to you?" and I did and it was happily ever after.
DS2 was 1, at DH's request after he went on and on and on about it from about 6 months onwards, and then I spent a bloody year and a half going back and forth to the room until I got strict with myself and stopped bringing him back in, then he slept through (after about 3 months of this)
DS3 I waited until 16 months but this time I didn't do the back and forth forever, I just did the no bringing him back through straight away, 3 months later he is doing much better at staying in his own room and has done one night with only a single wake up which is probably the best any of them have ever slept at this age.
Yes I know this is the wimpiest sleep training ever, it works for me though.
I maintain that it makes absolutely zero difference "having the bedroom back", it does seem to be really important to DH though. I thought it was a sex thing but not really. He just really likes being able to put the light on and stuff. I don't understand. But I was ready to put in the work at 16m with DS3, because I was getting fed up of night feeds.
Personally my motto is now if it ain't broke, don't fix it, and don't try to fix it unless you're actually committed to fixing it. It was so much more frustrating to go back and forth for over a year and that was stupid.
I think if you move him then you need to take turns with DH going back to put the dummy back in, but honestly I'd start strewing the cot with extra dummies and see if you can coach DS to get the dummy himself by guiding his hand to it rather than giving it straight to him, in the hope that he will eventually be able to re-dummy himself in the night and not need your input.