There are a few ways to go about it. Search this site for more information on this subject.
Search: Sleigh bed, cooper, coopered, coopering, wiggle wood(or board), bending, laminating... and anything else you can think of that relates to the subject. You will get more information then you will ever need.
Here are some ideas.
Coopering. This is when you stack several strips of wood to form the panel. Each strip is beveled to a particular angle to produce the desired rough curve. After they are all glued together, the panel is planed or sanded smooth to the desired finished curve. Barrels and buckets are examples of coopering. Darrell in Oakville posted a coopered sleigh bed quite a few years ago. I'm sure he has lots of helpful information but he's one of those crazy hand tool nuts.
Wiggle board is a type of plywood that bends very easily. It would handle that curve without issue. You would glue a few sheets together (if you want it thick)in a form for the desired curve and it would be covered with the desired veneer. The bow front dresser Edward G has for his avatar is an example of the use of wiggle board.
You could cooper a form using a cheep secondary wood for the shape and veneer it with the desired wood.
You could try steam bending but I think that would require some experience before attempting such a large project. You don't get a second chance. Mreza recently posted a bed with some steam bent and laminated parts. The panel was flat but there are a lot of curves else were.
Those are for the panel. The post would be cut out of a large board or laminated panel big enough to lay out the curve. Grain direction is important for strength.
Just some options to think about.
J.P. Rap Mount Hope Ont.
Carpe Ductum (Seize The Tape)
"In this world, you must be oh so smart, or oh so pleasant." Well, for years I was smart. I recommend pleasant. Elwood P. Dowd