I have a drop-side cot (Boori brand)- after doing some research online it seems the drop side cots are banned in other countries due to previous infant death. Should I get a new cot without a drop down side? Why are they legal in Australia if they pose a death risk to infants?

Red Nose recommends that the safest place for your baby to sleep is in a cot that meets mandatory Australian Standards.

Does your cot meet the standards? Is it new or second hand?

A safe cot is one that meets the Australian Standard for cots. All new and second-hand cots sold in Australia must meet the current Australian and New Zealand Standard for Cots (AS/NZS 2172)
https://rednose.org.au/article/what-is-a-safe-cot

Product Safety Australia (ACCC) develops & monitors safety standards in Australia.

Household cots are fixed sleeping enclosures for infants and babies. Cots can be rectangular with sides and ends made of slats or filler bars. Often one side drops down to give easy access to the baby. Cots can also be circular made with walls that have no slats. Some cots can convert to toddler beds.
https://www.productsafety.gov.au/products/babies-kids/kids-furniture/household-cots

Product Safety also includes the following information
Safe Use

If the cot features a moving drop side, ensure that the locking mechanism is functional and operates safely with repeated use.
https://www.productsafety.gov.au/products/babies-kids/kids-furniture/household-cots

Check that bars, panels, mattress base and drop sides are firmly attached.
https://www.productsafety.gov.au/system/files/Safety alert — Cots.pdf