Our 4 month old is in our room in a bassinet endorsed by CHOICE. We want to move him into a cot but it's too big to fit in our room and we want him with us until he is 6 months old. Is it safer to have him in our room in a bassinet or in his room in a cot?

You are correct. Red Nose does recommend Room Sharing for the first 6 - 12 months.

However, the baby’s sleep environment would take priority over Room Sharing.
Most bassinets are unsuitable for babies beyond 4 mths of age & a cot is important once baby is rolling.

https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over

Red Nose have 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.

Have a look at our full Information Statement here:
https://rednose.com.au/article/room-sharing-with-baby