However doctors cannot currently order Comirnaty "directly" from anywhere except from the government-controlled distribution system, which operates along the same basic distribution lines that are also used for other vaccines and medicine products, but is governed by special rules (for example the government can limit the number of doses a single doctor can order if demand outstrips supply).
And when it comes to ordering from the manufacturer, whether it's Pfizer or BioNTech, AFAIK nobody except nation states can do that. They just don't accept anyone else as customers - with very rare, but notable exceptions (there was this occurrence where the company TSMC ordered some millions of doses of Comirnaty as a proxy for the Taiwan government because some weird Chinese intervention, of which I didn't fully understand the exact mechanism how it worked, prevented Taiwan from ordering directly).