Perfectly normal. The first time I trotted was completely by accident and it scared the living daylights out of me...but at the same time, I loved it. The main reason it scared me is because I wasn't completely prepared for it (mare I was riding got a wild hair up her behind and decided to take off trotting, then cantering, then GALLOPING with me).
Now, I'd say it depends on the horse and how controlled their trot is, but trotting is definitely one of my favorite gaits. I schooled some horses at the Girl Scout horse camp last year (for some reason, whenever a horse misbehaved, I got handed the reins and was told to work the crap out her!) and I learned very quickly that not all trots are created equal! The horse I usually rode (Paleface, the non-kid-friendly, lead horse) had a beautiful trot for all her conformational faults and that's how we usually warmed up before a ride. On the other hand, Moon Dancer, who was a quarab, had the most bone-jarring trot I have ever ridden.
How old is your horse and how well-trained would you say s/he is? Is there anyone around you who has an older horse with a more gentle trot that you could learn to trot on? I know that that worked wonders with my comfort at a trot. Paleface was my confidence booster. I knew how to trot and could sit it fairly well, but Paleface helped me really develop my seat at a trot.
Well, her and Moon Pie, the big Friesian cross mare we had at the horse camp who felt like she was floating when she trotted. Lol