Hi Greener
The length you will need is approx 11 inches total length, and for draw boring you need to use green oak, and preferrably kept pliable by storing them in a bucket of water both before and after shaping is completed.
The taper should be approx 2 to 3 inches nicely done with a draw knife of hand axe--(not sawn)
It is preferrable to split the pegs out of straight grained white or red oak, this will give you a much stronger peg when completed because the grain will be running straight with the peg. Boughten ones will look nice but they may be turned out of oak stock that will fail under the drawboring technique.
to size them just pound them down through a 1" hole bored through a block of 1|2 or 3\4" steel plate, and if possible upset it from the bottom by heating the plate red hot and pounding a tapered punch in from the bottom, being careful to not expand the hole at the top. In the process you will notice the steel will bulge a bit upwards, this is good because it will peel the sides off the wood peg nicely.
It is not necessary to have the pegs perfectly round, in fact more rectangular or octagon is OK.
When you are pounding in the green oak pegs, and if the going gets tough, you may start to damage the ends of the pegs, so I usually wrap some
1\4" rope around the end before pounding to support the fibres in the end of the peg this is well worth the effort because it is almost impossible to remove a peg once it has started on it journey through the mortise and tenant.
It is up to the individual, but many of the old timers left some of the unsharpened end protruding, I personnaly like that idea, and in my own home I hang decorative things on these protruding ends.
Good luck on your project
The Northern Hewer