Copying a large plaster tile by latex moulding it; is my plan correct?
You're on the right path; the only things I would change in your plan would be not to remove the latex mould (often known as a print mould) before adding the supportive plaster mould (known as an overmould or mother mould). Shawn Thorsson's blog has a good tutorial on one piece moulds - he works in silicone rubber and plastic, but the principles are the same.

Plaster* and latex don't stick together much, so you shouldn't have any issues without applying talc or another release agent as long as you let the plaster dry for long enough, but there's no harm in applying one - the Hirst Arts website has a good guide to them.

Both latex and plaster do shrink a little, so consider applying multiple coats of latex to get the correct thickness when building the mould. Since you're doing a one piece mould, you can deal with the plaster shrinkage by over filling it and then scraping off the excess. Once again, Hirst Arts has a good tutorial on casting one piece plaster moulds.

*Admittedly my casting experience is solely with dental stone, which may be less 'sticky' than drywall plaster. Your mileage may vary.