Yes, unfortunately, it is common that doctors and even endos miss LADA; more frequently they misdiagnose it as Type 2. You have not been misdiagnosed. You are Type 1! LADA (I don't care for the term 1.5) is a form of Type 1 in which onset is more gradual and which occurs later in life. (I've got you way beat, I was (mis) diagnosed at age 58! Once the initial stages pass and our bodies stop making much insulin, we are, for all intents and purposes, Type 1's. The real differences between us and Type 1's diagnosed as children, is, imho, more psychological. I think there are things people go through when they are diagnosed with a chronic disease so young that we don't.
When I first figured out (myself with the help of this website!) that I was LADA, that distinction meant a lot to me, because I had worked so hard to arrive there. But I quickly learned that very few people knew (or frankly, cared) what it meant! When, after figuring it all out I finally saw an endo and presented her with my list of five things that made me know I was Type 1, not Type 2, she merely checked them all off and said, nodding, "You are Type 1". These days, nearly five years since my first diagnosis and 3 years since my correct one, I just call myself "Type 1". When occasionally, someone, such as m cardiologist made the assumption that I'd been Type 1 since childhood (with the attendant risk factors) I said that I was "adult onset".
Initially you will be managed differently because you are still making some insulin (have you had a c-peptide) but in time it won't make much difference.