Long time ago, I taught riding lessons to make some extra money. I only had one horse, but he was a good school horse, and I had six children who came weekly for their lessons.
One little girl fell off while learning to trot and absolutely panicked. She adored horses but she was terrified to trot, and I mean terrified. I was only 18 at the time, but I wanted her money and I wanted her to keep riding. So I promised her she would never ever NEVER be asked to trot. I told her she WOULD NOT trot until she had begged me to trot for 3 lessons in a row. (I guess I was a smart lil 18 year old). Every lesson, I had that little girl doing fun things at a walk. She learned to do gymnastics at a walk, she carried cups of water to pails, she jumped off in many different ways, did obstacle courses, learned to back up my pony all over the place--every week I came up with new things for her to do at a walk. She could ride standing up, backwards, and sideways. Every lesson, she would arrive saying, "I don't want to trot!" and I would assure her she wouldn't have to.
The other kids taking lessons were trotting merrily, then cantering, then doing little jumps, but this one little girl always walked. She was happy, and I was happy, and her folks were happy.
And then, of course, the day came when she begged to trot--3 times in 3 lessons, and she began to trot. At the end of the summer, I had a little exhibition, and she had pretty much caught right up with the rest of the kids I was teaching.
My advice is: walk as long as you want to. Do whatever is fun and gives you confidence and do not push yourself. You'll get there and it doesn't matter what the timeline is.