Is it safe for me to put a blanket on my 1 year old boy

Blankets can be used as long as they are light weight & tucked in firmly - not loose, and if there is no risk of baby’s head & face being covered. Most older babies/toddlers wriggle/roll, and do not stay under any covers, like blankets. They may kick blankets off, and wriggle underneath them.
The general recommendation for bedding for an older baby says to wait until a child is in a bed before introducing soft articles like pillow, doona or other soft or loose bedding.
https://rednose.org.au/article/safe-bedding-is-the-bedding-safe
https://rednose.org.au/article/sleep-baby-with-head-and-face-uncovered

Red Nose recommends to withhold the use of pillows until baby is in a bed & at least 2 years of age.
https://rednose.org.au/article/at-what-age-can-i-introduce-cot-bumpers-and-pillows
https://rednose.org.au/article/can-baby-use-a-pillow-to-prevent-flat-head

Older babies are at risk of “stacking” objects in a cot to help them climb from the cot.

A sleeping bag is probably the safest option when baby is rolling, as they reduce the risk of baby getting head/face covered.
https://rednose.org.au/article/safe-wrapping-or-swaddling-when-to-stop-and-how-to-select-a-safe-sleep-bag

When considering type of bedding for baby, it is important to consider the following:
Ensure baby’s head & face remain uncovered, the base (mattress) is firm & flat & that baby is placed on back for sleep.
https://rednose.org.au/article/how-to-dress-baby-for-sleep