Hi. When the time is right I was thinking of putting my baby straight into a single or king single floor bed. Is this safe/do you have a list of Sid’s safe mattresses? I understand they need to be firm. Thank you

For safety reasons, when a young child is observed attempting to climb out of the cot and looking like they might succeed, it is time to move them out of the cot.
This usually occurs when the child is between 2 and 3.5 years of age but could be as early as 18months.
https://rednose.org.au/resources/education

What age is your baby?
It is important that baby does not move from bed at too early an age.

Red Nose does not recommend specific brand name products.

You are correct, a mattress for a cot needs to be firm, clean, well-fitting & flat (not elevated)
Once a child is moved to a bed, at around 2-3years of age, they are well beyond the age of sudden unexpected death, so the requirements for baby in a cot are different.
However, a firm mattress would still be appropriate.
https://rednose.org.au/article/where-to-sleep-a-child-who-has-moved-from-a-cot

Don’t forget to check for possible hazards in the house.
https://rednose.org.au/article/making-your-home-safe-before-moving-a-child-from-a-cot-to-a-bed