Site identification survey for knockdown rebuild useful/necessary?

I am doing a knockdown rebuild in the Gold Coast area on a 800m2-ish block.

Should I get a survey done to confirm boundaries?

There is an old dodgy fence on one side that will probably need re-doing, so I am figuring there is no point building a new fence unless you are clear on where the boundary is. I am also guessing that council likes to know exactly how far the new building is from the correct boundary. And I am also guessing that maybe things weren't so precise when land developments were done 30-40 years ago.

My gut says, yes, get a survey done. Questions:
(1) What is the proper name for this type of survey - is it a "site identification survey"? Or is there a simpler and less expensive type of survey that might be sufficient for my needs?
(2) What do they typically cost?
(3) Is this the sort of thing that I should just leave to my builder (volume builder) to sort out?
(4) Should this be done before or after demolition?

I have been quoted around the $1900 plus GST mark by one surveyor I randomly contacted.