Our 11 week baby has started to roll from his tummy to his back during tummy time. He props himself up, leans over, and then lets gravity do the rest. Do we need to put him in a cot now? Or is only once he can roll from his back to his side/front?

Most babies will be rolling over by 4-5 months…....some earlier, some later.
This is very normal as babies grow & become stronger many babies then prefer to sleep on their tummy &/or side.
As he is rolling during tummy time, it is very likely he will start to roll when sleeping. This is not unusual at his age.
Are you still wrapping/swaddling him?
*It is important that you move him from bassinet to his cot now & cease swaddling.
*Baby needs arms free & the space of the cot to roll safely.

Once he is rolling it is important to make the environment as safe as possible for this to occur.
Continue to place baby on the back to sleep.
Ensure cot mattress is firm, well-fitting & flat.
Ensure there is nothing loose or soft in the cot.
Preferable to use a sleeping bag when rolling that has appropriate size neck & arm holes.

Red Nose has the following information when baby is rolling.
Give baby extra tummy time to play when awake and supervised as this helps baby to develop stronger neck and upper body muscles which in turn enables them to roll back over.
Make sure that baby is on a firm and well-fitting mattress that is flat (not tilted or elevated).
Make sure that baby’s face and head remains uncovered (do not use lambswool, doonas, pillows, cot bumpers or soft toys)

As babies grow and develop they become very active and learn to roll around the cot.
At this time, continue to put them on the back at the start of sleep time, but let them find their own position of comfort.
By this stage it is not necessary to wake during the night to turn baby over to the back position

*Do not use any devices designed to keep baby in a particular sleep position.
https://rednose.com.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over