My baby is 6 months old and has just started rolling onto her tummy to sleep. I place her in her cot on her back and she makes her own way onto her tummy. When sleeping on her tummy, her head is sideways, though her mouth and nose are very close to the mattress. I’ve tried to move her head sideways to better expose her face and she keeps moving her face back down towards the mattress. Is this safe?

Most babies will be rolling over by 4- 5 months. This is very normal as babies grow & become stronger.
Many babies then prefer to sleep on their side or tummy.
This is not something that needs to be stopped. It is important to make his new environment as safe as possible.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over

Have you ceased swaddling her?
Babies need their arms free & the space of a cot to roll well.
How does she go with tummy time when awake?
Is the cot mattress firm & flat?

Have a read of the Red Nose information now that she 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”
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over