Yes, QUARTERING is a Scrabble word!

Letter values in Scrabble US: Q 10, U 1, A 1, R 1, T 1, E 1, R 1, I 1, N 1, G 2.

Is it a valid word?

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

a coat of arms that occupies one quarter of an escutcheon; combining four coats of arms on one shield usually represented intermarriages
living accommodations (especially those assigned to military personnel)
dividing into four equal parts

provide housing for (military personnel)
pull (a person) apart with four horses tied to his extremities, so as to execute him
divide into quarters
divide by four; divide into quarters

Also: draw and quarter.