Is it safe for my 2 year old to have a blanket/quilt in his cot, he can now take his sleep sack off himself but isn't ready for a toddler bed?

Red Nose recommends to withhold the use of loose, soft bedding until a child is in a bed & is over 2 yo.
This is because some babies/toddlers will use any loose or soft items likes pillows/quilts to help them climb over the cot rails.
https://rednose.org.au/article/at-what-age-can-i-introduce-cot-bumpers-and-pillows

If you are concerned about him being cold, you can add an extra layer(s) of clothing.
https://rednose.org.au/article/how-to-dress-baby-for-sleep

Is he attempting to climb from his cot yet?
https://rednose.org.au/downloads/RN0407_22_Cot-to-Bed.pdf