Pfizer's CEO answered this question this morning on CNBC.
Pfizer has two separate manufacturing divisions- one in the US (Massachusetts, Missouri, Michigan) and one in Europe (Germany+Belgium).
They will be producing in parallel and he seemed to imply Europe manufactured->Europe distributed and US manufactured->US distributed initially (but didn't explicitly say this). But he then stated that it's important to share the vaccine across the world - "I hope that we will be able to ship to the entire world from these manufacturing sites without problems".
They have signed contracts with multiple governments in the world and in most cases have defined their monthly quantities distributed to those countries through 2021. I would guess these are public and am curious about the quantities and timelines for the various countries.
They are estimating to have 1.2 billion doses by the end of 2021 (enough for 600 million people, as each person needs two doses).
EDIT:
US: 100 million doses of this Pfizer vaccine (enough for 50 million people) by December 2020[1], but Pfizer now says they are only producting 50 million doses globally this year[2]
[1]https://www.nytimes.com/2020/07/22/us/politics/pfizer-corona... [2]https://www.pfizer.com/news/press-release/press-release-deta...