Will I have to claim bags at FCO?

If you booked your flights with United and they’re on one ticket then check with United.

If you proceed to IAD without entering Italy, there is no need to retrieve your luggage. It will proceed to IAD. Only the US government requires retrieval of luggage and re-check in at the first port of entry.

Malta is part of the Schengen zone, so you will do Schengen exit passport control at FCO, but your bags should be checked through to IAD. You will do US immigration/customs when you land at IAD.

Since it is on one booking, your bags should be checked through, however I do not see them listed as a United partner.

You could certainly verify with whichever airline you booked with (unless you used some third party site).

1:45 certainly would not be enough to land, exit security, retrieve bags, go find the United bag check, and go back through security.

When checking in at MLA, you will though be able to verify by the tag.

I booked as one ticket...

Well that is the critical bit, and all depends on that being correct. It would be wise to carefully verify that this really is indeed the case - a single ticket (with multiple legs).

If you bought the ticket directly from United or KM Malta, then you are probably good to go. If, OTOH, you purchased from some no-name (or even a big-name) "online travel agency" (OTA) then check very carefully, as OTAs often cobble together a "franken-ticket" itinerary by stitching together multiple tickets and then selling that to you. If you have more than one actual ticket, then there would be no chance of the smooth handoff of your checked baggage.

It would be good to confirm that (it's definitely a single ticket) now, not at the airport when you try to check your bags all the way through.

Thank you all for your responses! I booked the flights directly with United. Fingers crossed that my bags will be checked through to IAD on my return.

Thank you all for your responses! I booked the flights directly with
United. Fingers crossed that my bags will be checked through to IAD on
my return.

If you have any doubt, just ask the person at the counter when you drop your bags. And look at the tag they put on the bag. Should say IAD.

Thanks again all, I confirmed with KM Malta. My flights are under one ticket number and they have an agreement with United, my bags will be booked through to IAD.
Happy New Year!