We have been given a cot that has been passed down in my husbands family that his grandpa built. It had a drop down mechanism and I have been reading about how they are dangerous.. Should I be using a cot with a drop down feature or should I buy a new one?

Red Nose recommends the safest place for baby to sleep is in a cot that meets mandatory Australian Standards.
https://rednose.org.au/article/what-is-a-safe-cot
Drop-side cots are included in 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

It is unlikely that the cot you describe would meet Australian Safety Standards, due to its age.
Most safety experts, including Red Nose would recommend buying a new cot that meets the standards.
https://www.productsafety.gov.au/standards/household-cots