I have a porta cot (to use when we are away from home) that has a very hard base and does not have a mattress included. In the instruction booklet there are recommended measurements if one is to be made. Would having a mattress made to those specific measurements be safe?

Is this a new portacot or previously used?
Does the cot meet Mandatory Australian Standards (2195)?
How old is your baby?

Product Safety Australia (ACCC) has the following included in their safety information for portable cots.
Have a look at full info in link, especially if this is a pre-used cot.

If you need to buy a mattress, get one from the supplier that meets the specified dimensions.
https://www.productsafety.gov.au/products/babies-kids/kids-furniture/folding-cots
https://rednose.org.au/article/portable-cots