Yes, POSTDOC is a Scrabble word!

Letter values in Scrabble US: P 3, O 1, S 1, T 1, D 2, O 1, C 3.

Is it a valid word?

POSTDOC is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

a grant that funds postdoctoral study or research
a scholar or researcher who is involved in academic study beyond the level of a doctoral degree

Also: post doc.