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The most expensive tool is the one you buy "cheaply" and often...
Stand for something, or you'll fall for anything.
Properly glue and clamped, this crack will be invisible and as strong as if it had never happened. There is absolutely no reason to remake it
This.
And no need at all for dowels; they just add complexity & would look weird. Just make sure the pilot bit is sized right. It should be the same size as the root of the screw, but with some hardwoods, you may need to go up a size. Use an off cut of the same wood to test for pilot size.
Repairing it is perfectly viable, especially since it is for you. I would sand and refinish the end after blowing in some glue, removing the screw, clamping and letting it sit 24 hours. It should be hardly visible.
I also agree with the comments about strength for racking loads. Vertical loads - the main load on the leg - it doesn't matter how long the leg is. But if you move the bed and sometimes when you move on the bed, it wants to lean the legs. When that happens with a leg with so little material above the screw, it will want to crack again - or crack another leg. But it may not happen. So I would glue it up, refinish the top of the leg and hope for the best.
I only use these type of bed rail fasteners after trying several types. I never put a dowel in but I do use as long a screw as possible. Same thing on the end of the rail. Some of the beds I've built this way have been used for a decade or more at this point and all work fine - no issues. So I do not recommend adding any dowels. But I would use a minimum 2.5 inch screw for the screws into the rail. Holding power in end grain is not as good but with a good long screw it is still fine. In the leg you are going into long grain so I don't understand why anybody would dowel that - waste of time in my opinion.
Couple additional suggestions, when you insert and tighten the screw, clamp the piece so the screw can't force the crack open and add low friction furniture glides to the bottom of the feet to minimize racking stress on joints when moving (added bonus it protects floor if hardwood).
1. Cut a slot through the crack, and then glue in a spline (as already suggested)
2. Cut 2 or 3 slots perpendicular to the spline and glue splines in those cuts.
3. Drill pilot holes as large as possible to still get a good grip on the threads. Check first on a scrap of similar wood.
I find the wide range of opinions and options really interesting! Great to see so many different approaches to any given situation.
For now, I've glued and rescrewed. Worst case, I'll replace the leg, which really isn't THAT much work.
You did what I would have likely done, Aaron. I doubt it will fail again but as you say, if it does, there's a remedy.
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The most expensive tool is the one you buy "cheaply" and often...