Another month shouldn't matter; "or so" might.

Get the kit, and let's find out what you're dealing with. If you have no CYA and no ammonia (I can tell you how to test), then you can wait. If you have CYA, not so much; what hasn't gone wrong yet, could soon. If you have ammonia . . . better start now.

Otherwise, your family may go buy a hunting license for your hide, when the pool is not open and looking nice on the expected date = first really warm day in spring, usually. Trying to clean up an ammonia mess in a hurry is no fun: just check out some of the posts we'll get in May from that.

BTW, a lot of folks here tend to think BBB = bleach, but it's my method, so I feel free to disagree. Bleach is just ONE way to do pools; when I started PoolSolutions (which preceded the PoolForum) bleach was cheaper, relatively, than it is now. Bleach has benefits, but so do other materials. Dichlor, trichlor, cal hypo can all work well IF you understand what they do and how to use them.
(Not lithium hypo, and those AWFUL some form of chlorine + GOOP shock blends they sell today). I currently don't use bleach on my remaining local commercial customer -- it's not practical for me, since I no longer need truckloads of it -- but use a blend of SWCG's, dichlor and trichlor.

Bleach is STILL probably the cheapest chlorine material you can buy in small quantities, but it's not nearly as cheap as a 50# bucket of dichlor or 40# bucket of trichlor at Sams. Cal hypo is now hard to buy inexpensively, and is a tricky product to use well - but it works really, really well if you know how.

So, find out what you've got, and while we're waiting, check and see what's available to you locally (Sams, Walmart -- no blends!!! --, Lowes, etc.)