My baby is 5 months and 10 days old. He's been sleeping in a travel cot in our bedroom per your recommendations, however he's started to wake up through the night when my husband or I move / get up to go to the bathroom / cough etc. My sleep consultant suggested it might be time to move him to his own room which I'd like to do, but wanted to check that it's safe to do so when he's not quite 6 months yet. He has no health issues and is strong and good at tummy time. We don't have any other risk factors (I don't smoke, we haven't been co-sleeping etc). Appreciate your guidance. Many thanks, Lauren

Red Nose does recommend Room Sharing for the first 6 - 12 months as a way of reducing the risk of Sudden Unexpected Death in Infancy (SUDI)

However, the baby’s sleep environment would take priority over room sharing.
Many parents are unable to room share for more than a few months.

Do you have a standard household cot for him in his own room?
Is he rolling yet?
Are you still wrapping him?

Red Nose has the following information
Parents are not expected to observe their baby constantly. 

If your baby is sleeping in a separate room check baby regularly to ensure that the baby remains on the back and the head and face remain uncovered (as baby grows beyond 5-6 months they will move around the cot and roll over; settle baby to sleep on their back but let them find the sleep position they feel most comfortable in. 

A safe cot and safe sleep environment is still necessary for babies older than 5-6 months)

The protective effect of room sharing can be partially explained by increased adult supervision and observation of the baby.

Room-sharing facilitates a rapid response to a baby’s needs, and supports breastfeeding, and is more convenient settling and comforting of babies. It also provides closer mother-baby contact and communication
https://rednose.org.au/article/room-sharing-with-baby