I pack and transport more than a dozen antique treadle machines at a time, a few times each year.
I strongly recommend taking the irons apart. Cast Iron is VERY fragile. When it is assembled it is a self supporting structure, but it is designed to support the weight pushing down. Sideways or diagonal impacts can/will snap it like a dry twig.
MOST treadles some apart very easily. (and go back just as easy)
My usual sequence is:
1. remove head from unit
2. remove the screws holding the top to the base
3. Remove the drive wheel (big one)
4. Remove the Pitman (wood/metal connecting rod from pedal to big wheel)
5. Remove the cross support
6. remove the pedal bar and pedal.
Pack each with padding or blankets between them, stack them, then bundle the whole stack with clingwrap
Pictures of YOUR specific model of treadle would let me give more specific instructions.
HINT: when you remove a screw/bolt/nut, once the parts are separate, put the screw/bolt/nut back where it came from. REALLY hard to lose or mix up the bits that way