My 9 week old is turning in his bassinet. He is swaddled in a love to dream swaddle. Is it time to move to the cot? And is it unsafe for him to be in that swaddle with so much movement?

We have had regular questions in relation to babies rolling at an early age.
Most babies don’t roll intentionally till about 4 months - some earlier, some later.
Regardless of age it is important to make some adjustments as you would if he was older.

Red Nose recommends always place baby on back to sleep.
However, there seems to be a number of babies who wriggle/roll to their side or get out of their wrap, at an early age, as you are describing.
Sometimes it is because these babies do not respond well to wrapping, & are less likely to roll when unwrapped, (ie both arms out)
At times babies like to touch their face when sleeping.
As he is starting to roll, it is time to move his from bassinet into his cot.

All swaddling/wrapping (muslin wrap or swaddle suit) should be ceased when baby is rolling.
https://rednose.org.au/article/is-it-safe-to-wrap-swaddle-my-baby