New to Hydrea for ET

I am a 73 year old very active woman who was recently diagnosed with Essential Thrombocythemia by having a high blood platelet in a CBC and then a bone marrow biopsy that confirmed the diagnosis with a CALr gene. I have no symptoms and am on no medications for anything else except for a yearly infusion of Reclast for the old bones. I run most days of the week and work out at the gym.
My oncologist hematologist says I will start on 500mg of Hydrea when I get back from my monthlong trip to sunny Costa Rica. Right now I’m just taking a baby aspirin. I’m not so afraid of the cancer as I am the treatment. I can overcome a lot of things but one I can’t is the fear of losing my hair. I’m just going to say this is all about vanity. I haven’t read much on this forum about this possible side effect. I’m looking for reassurance that this is a rare occurrence. I hope you can help. Thank you.