Walkaway split or were you thinking of buying a queen? It would be 28 days after a walkaway before you saw any new eggs and another 21 days after that before you started seeing new bees. I wouldn't be hesitant to do a split with a new queen.
It does, colony hasn't reached peak strength, brood area not fully available, space still being taken to store nectar spread across the entire frame instead upper corners, and cross top of frame. Once the queen can fully utilize both brood chambers, and lay a full brood cycle you notice a startling increase in colony strength, have supers available lol.