Is there an age at which letting a toddler have blankets/sheets/quilt is deemed fairly safe?

Red Nose generally recommends that you withhold any soft or loose bedding until a child is out of a cot.
https://rednose.org.au/article/at-what-age-can-i-introduce-cot-bumpers-and-pillows

However, heavy adult bedding may not be suitable for toddlers.