The headstock is the piece that will hold the turning mechanism (hardware) and support the work-piece of the lathe, so it should be very strong.
The thickness of the headstock is according to the mandrel and pulley size you will use.
It can be made of thick pieces of hardwood (if you can get your hands on any) or it could be two pieces of plywood stack together which is also makes it very strong.
My design of the headstock starts with thick T shape hardwood which is 15cm (6" wide), 16.5cm (6.5") high and deep enough to take the mandrel base. You will need two identical pieces of these. Then there's the middle piece which has the same length but shorter so that can give allot of clearance to the pulley and the belt, and its thickness is bigger than the pulley's steps. These 3 major wood pieces can be also be made from plywood. Everything needs to be well glued and screwed together solidly.
The headstock mechanism consists from a double ended mandrel with its bearings, a shaft and its locking collars, the second 3 step pulley which goes on the center but facing to the opposite direction from the motor's pulley, and a strong drill chuck at the end.
Now all these have to be found from your local suppliers or the internet and match together before you can build the headstock.
The mandrel is to be fastened down with 4 bolts and nuts into threaded inserts that will go into the wood.
In case you are wondering if you can avoid the mandrel, then I will say that you could make the two edged pieces taller like two towers, drill holes to accommodate tightly the two bearings (bearings need to fit the bolt diameter), use a long bolt without threats to go through the 2 tower pieces (needs to fit the pulley opening), file the bolt flat to the areas that the locking collars will be tight down, and mount the drill chuck to its end.