First, I would look into a new pediatrician. You asked yours a question and you got a lecture about her kids? Um, not good. But honestly, I suspect she's right that nothing is wrong, and your child is just growing quickly and needs his sleep.
Some kids do need more sleep than others. There could be other things going on as well, though, especially if he appears tired during his waking hours as well. Do you make sure he is getting lots of iron (protein) and carbs? Carbs and protein are where our energy comes from, so make sure you're feeding his brain. At this age, he should be eating several table-spoons worth of oatmeal, wheat bread, or pasta at every meal, and also at least 1 container of yogurt a day (meats and veggies and fruits are important, too, of course). If you know for a fact that he is getting all the natural sugars and proteins he needs, then you might consider having his blood tested for anemia, just to rule it out.
However, I suspect nothing is wrong. You might try pushing your son's bedtime back to about 7 (6 is a very early bedtime for a 1-year-old) and you can fill the time with a bath, story time, singing lullabies, etc., and make sure you get that extra snuggle time in there. But if you don't think your son could hold out for another hour, don't push it. If the behavior continues for more than a couple more months, then I think it would be time to seriously investigate what's going on. Good luck.