I never felt I was in the wrong body either; I hated my body, hated the male role, and always had that nagging wish that I was born female.
I've had many doubts throughout this whole process. I've probably doubted everything at one time or another...For years I doubted if I was even trans.
I started off transition by doing the things that I had the least or no doubts about. Luckily for me, one of the first things I started was hair removal. Always hated it, hated shaving too, and knew I wouldn't miss it if it was gone. Figured it wouldn't out me either and I could always stop if I wanted to.
I knew I wanted hrt yet had many doubts about that. I had already kinda messed around with it (self med herbs, I'm bad I know!) and I liked the changes I saw from that. I was also really depressed, kinda suicidal, and I knew I had to try to fix self. I really had no intention of coming out or living part or full time at the time, identifying myself as nonbinary back then. Worried I was way to manly, too old, and that hrt wouldn't help me enough to ever be passable. I worried that it would be too effective too, that I would have male fail and everyone would be able to tell. I was worried I wouldn't like some of its effects on me, how I would feel on it. I decided that I would deal with it if/when these issues came up, no point worrying about it nonstop in the meantime.
Doubted that I'd ever come out. I had much shame and embarrassment about it and I had spent my whole life doing everything imaginable to avoid those two things, needing everyone to see me in only a positive light, to like and respect me. Eventually, thru either a need within to tell people, or by being slightly outed at work, I came out to most, very slowly mind you.
I doubted I'd ever go out in public. This was mostly based on fear I think. I wanted to tho, kinda felt I had to too (safe place only, doc, therapy, group). As I continued doing so, experiencing no negatives, world not ending type thing, felt more comfortable, confident, happy doing so.
I'm currently undertaking another huge step; name change, and got massive doubts and fear creeping in yet again. Feels like a massive undertaking, and a scary and permanent step and all. I know how I feel about being called dude name tho, it bothers me, upsets me, depresses me, and if done in public (doc or something official like that), outs me, which I hate. I also feel really good when I'm miss'd and girl named yet I'm still worried.
So ya, I think doubts are normal and to be expected. We are undertaking a huge thing, venturing into the unknown, making life changing decisions that carry real life repercussions.
As to when they go away; for me they go away as I face em, as the unknown becomes known, as the different becomes the new normal. Here I am, basically full time (depends on your definition of ft, personally I call myself ft, some may not) female and for the most part, doubt free. I know how I am now, I know how I feel now about myself, and I can't for any reason see myself ever going back to where/how I was before.