A support set beneath a thing to keep it standing. First a stake under a growing vine.
Middle Dutch proppe (a support, a stake for a vine), of further origin honestly uncertain beyond that Low Countries root; a prop was first a stake set under a growing thing, and the sense of any support follows from there.
A support placed beneath a thing to keep it standing upright. The oldest image — a stake under a vine — is the right one: a prop holds up something that is alive and still growing, not something finished.