It wouldn't even be very difficult. You would want to code it in brainfuck and then translate, and the internal representation for each command should be a pair of numbers (probably from 0-2) to represent the punctuation of each half-command. You could borrow much of the structure from Erik Bosman's brainfuck quine.
Updated: here. https://gist.github.com/danielcristofani/1fe53487df1f7afcb5b91c06d95184b2
This is ~40 commands taken directly from Erik Bosman's quine, another ~120 freshly written commands of rather clunky output code to handle Ook!'s verbosity, and then the data segment to represent all that.