The Oxford Latin Dictionary gives Cicero as the oldest source for imperium used to mean "a particular instance of dominion, an empire." He doesn't use Romanorum though; he uses forms of noster, though that probably isn't a meaningful difference. Pliny the Elder uses Imperia Romanorum Parthorumque, so that's closer to what you're doing. Tacitus uses Romani imperii.

Imperium in the sense of dominion in general is as old as Cato, who used it with a form of noster in his histories. That's basically our oldest prose. Virgil is the first poet listed to use it, which also isn't surprising.

If I may ask, what purpose are you thinking of putting this information to?