Fiumicino has two terminals in regular use. ADR's terminal page lists them by airline: Terminal 1 for domestic and Schengen flights and Terminal 3 for flights outside Schengen. It does not describe how they connect, but third-party guides call them a short walk apart.
Which one you need
Check your ticket. We could not confirm from ADR's pages where Qantas or Emirates fly from.
What it means for a hotel
Every hotel here is reached from T3. The Hilton Garden Inn shuttle and the Best Western shuttle both pick up at the T3 arrivals area. Hilton Rome Airport is on foot from the terminals through a covered tunnel. See our short lists for Terminals 1 and 3.
Terminal 5
Older guides mention a Terminal 5. ADR's pages do not, and sources disagree on its status. Treat it as closed unless your ticket says otherwise.