Good to know your OK. Wishing you a speedy recovery and thumbs up for wearing your gear.
Shit happens and consider it a part of the learning curve to riding safely. You will learn from this and become more experienced...it happens to everyone.
I had a similar situation back in 04. Just picked up my 998 and 2 weeks later a dumbfuck rear ended me at a stop sign...fortunately the bike had minimal damage and i rode it straight to the dealership in Melbourne, Australia called Moto One.
They assessed it and told me they would right it off as it had less than 200klm on the clock.
I allowed them to deal with the insurance guys (fortunately the driver was insured) but i had to be on their backs constantly...making 4 to 5 calls to the assessor every day until i got my pay out.
They also replaced my Arai helmet, Dainese jacket and gloves as these were also new.
I'm not sure how it works in the U.S but you've got to hackle the insurance company otherwise they will let it slide for months.
Good luck to you and hope your back on a ducati again soon!