Great question, since I struggle with that too. I never call her by her name, really never. She certainly wants me to use her first name, she has askes me to do it several times, but i just cannot. it would feel horribly weird.
She signs het emails with dr. First + Last name. I really hate that, and I find it quite ridiculous too (oh come on, her full name is in the mailaddress already!). So in my replies I start with "Dear dr. First + Last name. It looks very silly and by some of her remarks I know she hates that too
But we seem to be on these terms now and as long as she doesn't change that, I won't either.
Maybe a bit off-topic, but I really go like crazy when she uses my name, too.