Leave it until October:
https://www.rhs.org.uk/advice/profile?pid=293
Small fir trees are remarkably tolerant to being transplanted though, even in midwinter. When I was a kid, my day would always buy a
rooted Christmas tree, rather than a cut one. Once Christmas was over, he'd plant the tree in our front garden (with no preparation whatsoever, other than digging a hole for it) and leave it there until next December, when it would be uplifted again for Christmas - being temporarily planted in a pot indoors - before being replanted outside again in January). Each tree would last at least 5 years before eventually succumbing to the stresses of being moved once too often, so I reckon that the chances of your similarly-sized tree surviving a single move at the right time of year (and with proper preparation of the soil, rather than just digging a hole) must be pretty good!