We have a 16 month old child start at our child care centre -who has a sleeping bag with no arm holes and the arms are tucked inside the bag. Is this safe for that aged child to sleep in this kind of sleeping bag while at the centre? Or is an arms free sleeping bag a safer option for this age group?

Red Nose has the following information in relation to swaddling/wrapping or using a swaddling suit (with arms in) as you describe.
Swaddle suits are not recommended by Red Nose for use once baby is rolling (usually from 4-5 mths of age)

It is essential to discontinue wrapping as soon as baby starts showing signs that they can begin to roll, usually between 4-6 months of age but sometimes younger. Babies must not be wrapped if sharing a sleep surface with another person. Baby should not be wrapped while sleeping in a baby sleeping bag.
https://rednose.org.au/article/is-it-safe-to-wrap-swaddle-my-baby

ACECQA has the following information

Sleep and Rest Practices.

If a baby is wrapped when sleeping, consider the baby’s stage of development. Leave their arms free once the startle reflex disappears at around three months of age, and discontinue the use of a wrap when the baby can roll from back to tummy to back again (usually four to six months of age). Use only lightweight wraps such as cotton or muslin.
https://www.acecqa.gov.au/resources/supporting-materials/infosheet/safe-sleep-and-rest-practices