Hi! My 13 month old has moved from cot to mattress on the floor. Is there any advice about the use of blankets as the weather gets cooler (eg tucking under the mattress as would be done in a cot)? Many thanks

Red Nose has the following general information about safety when a child is sleeping on a floor mattress

Ensure the mattress is positioned away from the walls as young children can become trapped bet ween the mattress and wall.
A child’s mattress needs to be firm to prevent sleep accidents.
Keep the area around the mattress clear of soft toys, bean bags, plastic bags or similar objects that a young child can roll onto.
Soft objects could mould around a young child’s face, resulting in suffocation.
https://rednose.org.au/article/where-to-sleep-a-child-who-has-moved-from-a-cot
A child no longer sleeping in a cot has greater access to all living areas. Before your child graduates to a bed, check your child’s room and throughout the house for possible hazards.
https://rednose.org.au/article/making-your-home-safe-before-moving-a-child-from-a-cot-to-a-bed
As far as blankets are concerned, it would be preferable to have them tucked in, but often toddlers move out from under blankets.
Sudden Unexpected Death in Infancy (including SIDS) does not occur after 12 months by definition, so the issues about safety in sleep are more about accidental injury once a child is over 12 months.