Parents don't always show how worried they are, and your father may wonder if you are ok. Knowing the truth may be a relief to both of you. You get the relief of not worrying about when to tell, and your father will finally know what is going on.
Telling my father was hard, because even though the signs were there, I was the only "female" of three children, and his 'little girl". I had asked my mother to tell him, but she said she wanted it to come from me.
There really isn't an easy way to go about it, and I think the majority of transgenders go through a certain degree of fear of rejection. No matter how old we are, we want our parent't approval, not just on this subject, but on what you do with your life in general. That is natural.
If you can get through telling your parents, then you can get through everything else that follows.
sam1234