This answer might be a bit might "longish" because this question can't be answered with a simple date...
On SIDS in general:
First things first: SIDS has been a subject of extensive research, but there is still no "final" answer what causes it. Statisticians have gone wild on potential risk factors, determining an entire list of what increases the risk of SIDS. I'm not going to repeat this here, there is plenty of material available online.
You are correct in your assumption that young babies should sleep in the same bedroom as their parents, A E has given a bunch of useful links in his comments above, so I won't repeat this here either.
In theory, your otherwise healty, breastfead baby is at minimal risk if:
- He/She sleeps on his back in a sleeping bag
- He/She sleeps on a rather hard mattress in his/her own cot
- His/Her bed does not have cushioning, fluffy blankets or stuffed toys
- The parent is non-smoking
Note: No time frame given for this risk-reducing factors.
So far, so good. Should your baby agree on these terms, congratulations. Mine didn't.
This is how it went for us:
As a first parent, I meticulously placed my baby on its back in the crib / stroller /... - where he would either not fall asleep or wake up really soon. He slept fine on his stomach or on his side. With hindsight, I could have realized sooner that both parents prefer to sleep that way, too... Was the same with child 2.
Also, child 1 slept almost exclusively with body contact, from day 1 on in hospital (after 53 hours of labour and a C-Section, no less), so not co-sleeping simply didn't work for us.
Was I worried? Sure I was. Especially as a first parent one is inclined to follow each and every advice and to do everything by the book. What calmed me was that the absolute risk for SIDS is not terribly high for healthy babies and that we did what we could to avoid the risk factors our babies agreed upon too - no overheating, no smoking parents, breastfeeding,...
Some practical advice on co-sleeping or sharing a bedroom
You ask when you should move your baby to his own bedroom to decrease the risk of SIDS.
There is no reason to move your child out of the parents bedroom to reduce the risk of SIDS.
You could argue that the risk of SIDS is the highest between 2-4 or 2-6 months and is only minimal after the first year. So you might conclude that sharing the bedroom is not necessary any longer (with regard to SIDS-risks) after 6 months or a year. There are other reasons why you might want to continue these sleeping arrangements, but discussing them here would be definitively off-topic.
But I can understand the wish of having your bedroom to yourselves again. You are not only parents, but a couple, right? This has been discussed here, for example. One word of advice: Bedroom activities need not be restricted to a bedroom...