as much as i hate to buy queens, that's probably the way to go at this time of the year. you want to give your split a chance to build up a bit before the weather changes. they need younger bees to make it through. if you allow them to requeen themselves, you won't have new brood for weeks. i'd also be sure to give your split brood in all stages. maybe skip the eggs, but go for the larvae that's a few days older and some capped brood. you'll probably want to feed them also unless you can give them some frames of honey. even then, you'll have to watch that they don't use it and have enough left for winter.
+ you are probably in an AHB area? buying queens might be safer for you and will give you some new genetics in your yard for next year.