we got an extension built a few yrs back over our side garage & utility and the 2 new bedrooms were to be accessed by the opening like yourself, at the top of the stairs.
The builders worked outside first building up the extension. Then cut the wall from the outside and did all the dirty work outside in teh extension, cutting into the blocks and removing them there. Then they punched through the plasterboard from the inside. Steel lintel had to go in to support the opening.
Be careful about one thing. The height of your floor in your landing may not match up exactly with the height of your new floor and you may end up with the levels not being the same between the new room floor and your existing landing floor. TBH, there is nothing you can do about it. Mine was an inch higher on the extension side..hardly noticeable