Moody's wording in ch86 seems to imply the Order may not have even existed before Monroe 'died':

"Flush of gratitude and all that," Mad-Eye Moody said sourly. "It didn't last, but at least James and Lily got a fancy title and a useless medal to take to their graves. But that's leaving out eight years of complete horror after Monroe disappeared and Regulus Black - he was Monroe's private source in the Death Eaters, we're pretty sure - was executed by Voldie. Like a dam breaking and gore flooding out, drowning the whole country. Albus bloody Dumbledore himself had to step into Monroe's shoes, and that was barely enough for us to survive."

(Although you could argue that Monroe had formed and was the head of the Order, and that is what Moody meant.)