Did a bathroom years ago. Bit of a nightmare, and pretty expensive.
- Do we just get a 'builder'?
If you have the time, tools and skills there's no reason you can't do a fair bit of it yourself.
- Do we get a specific 'bathroom renovation' person?
If you do get someone in I would get someone that does bathrooms. There are specific requirements under the building code as I remember. Things like damp proofing around the bottom of the walls and shower alcove.
- Who does the 'design' of a bathroom renovation?
Your wife! 
You can get good advice from places like Beaumont Tiles (I don't have any association with them. They were good when we did reno, and when we built a new house).
- How can we save money? Demolish ourselves? Re-tile ourselves? Buy kits, or new toilet, or cabinet etc from Bunnings?
Bunnings have toilet sets, etc. Some of their stuff is good. Some not so good. We demolished our internals walls, ripped up old tiles & motar bed, & put up new wall linings and cornice. Had tiler come in because I didn't have time, and also to do the damp proofing, then we did the painting and fitoput of screen, cabinet & tapware.