We are just night weaning our DS (17 mths). He was waking 2 or three times in the night and needing a bottle to go back to sleep (as well as his bedtime bottle; I stopped bfing at 13 mths). It was so easy just to do it as once he had had it you could just pop him back in the cot and he was quite happy to go to sleep.
But I think it was not helping him to sleep through and he was learning to feel hungry and wake a lot. And we were fed up with faffing around with bottles in the small hours.
We are on day 6 today. He has already forgotten the association with the bottle and now just looks for a cuddle and then (depending on how tired he is) someone to sit with him with a hand on his back until he drops off.
Results have been mixed. Last night he slept through! The night before he woke 4 times loads but settled v quickly each time within a couple of mins. The night before that it was a couple of wakings needing about 15 mins to settle each time. The night before that was an odyssey with three wakings needing about 40 mins to settle each time. So we have definitely made progress given that a week ago this was a boy who would howl for a bottle and would be waking three times a night.
Given you are bfing that adds a different element to the mix - could you get your other half to do it? At 12 mths too he is a bit young to understand "boobies asleep" or "bottle all gone". With my DS I could tell him I was going to sit with my hand on his back and he would understand, but I don't think your DS would.
So I think maybe the best thing would just be pick him up when he cries, cuddle, and put back down in the cot with your hand on him, talking softly and reassuring, then sitting there till he calms down. Keep repeating and repeating each time he stands up (does he stand up?) and eventually he will give up.
But be warned he will be very cross at first and it might take a few nights to get through it. And there is no guarantee he will sleep through, but at least you are breaking the association with feeding and putting him in a position where at least he is in a good position to start self soothing. That would be impossible while you still have the feeding association in place.
My daughter slept through reliably from about 20 months, they do it when they are ready. Before that, from about 15 months, we would have some great nights, some OK nights and some rough nights, with the general trend being towards things getting better. All I think you can do is remove unnecessary obstacles so that when they are ready they are well placed to do it.
I wouldn't do CC personally. It's just my own view but he is still relatively young (big difference between 12 and 18 mths in terms of what they can understand about concept of time and whether you are coming back etc). And using the gradual withdrawal method that I suggested above is probably no more time consuming to you or stressful than CC - you can either sit with him and comfort him or wait downstairs while he howls on his own, feeling terrible with your stress levels going through the roof. At least with gradual withdrawal you feel less anxious as you know that although you are taking away their prop you are not leaving them alone and are trying to do it as gently as possible.