Thats a lot of changes you want to make in a relatively short space of time.
As she is that bit older it should be easier to explain the need to go slowly.
Name change, no problem. Hair cut, no problem.
Doctors, should probably put off for a good year or two. Once you get the appointment at the gender clinic (which will take months) it goes fairly quickly, and once hormones are involved there is a lot of irreversible damage, even if detransitioning.
I found videos of the actual operations, stories from detransitioners, and every negative thing I could find, and explained to my child every consequence that could possibly come from this and we have been through every horror story and discussed them at length.
Now, more than a decade later, my child is still 100% sure, my child was much, much younger than 16, and we are now tentatively taking the first steps (after a lot of counselling, a little through the NHS and a lot privately funded by me).
Its great that you're supportive but there is a very fine line between supportive and encouraging, and you don't want to get into the situation where you're pushing it under the guise of being supportive. I found myself falling into this trap a few times, its easy to do.
Its really difficult, but its a path that lasts a lifetime so its much better to be totally sure before taking drastic measures. Take some time to get used to each step, and just remain supportive, and read and learn everything you can.
Its not easy 