I certainly am not a professional but I have a son that isn't much of an eater, too. He wasn't losing weight, but has always been in the <5% percentile. My comments are based on when my son was at least 18 months; a newly turned one year old is still transitioning not only to new foods but to the idea of eating them at all.
We went to see a nutritionist last year and one thing she pointed out is how much liquid my son was consuming. She reviewed his typical day and pointed out that since I was giving him 8 oz. or so of milk first thing in the morning, he was too full from that to eat breakfast. Then, I would make him a smoothie for a snack, and it was pretty big, too. She saw that even though I wasn't putting as much liquid in the smoothie, it was still ending up as a large drink and that was filling him up so he'd refuse lunch. The pattern continued all day - he wouldn't eat, but would have a drink like milk with his snack/meal. That liquid filled him up too much and he was never really hungry, just topping off all day.
She had me limit him to 4 oz. of anything (except water - he can have as much of that as he wants any time!) at one sitting and to try to not give him the drink until after a meal had started. I measured what that would be in his sippy cups and it was way less than what I was typically serving. So I still stick with that rule now. He doesn't drink that much juice, but I did manage to find juice boxes that are only 4 oz instead of the normal 6 oz or 8 oz sizes.
She also told me to stick with set meal and snack times (3 of each) and to always have them at a table. No more grazing! No more wandering around with a snack and again topping off all day. He needed/needs to learn that eating isn't something you do when you're doing another thing - it IS the activity. I think that creates healthy eating habits, too.
I'll admit he still doesn't eat much but the rules really did help and I've learned to just not worry about it. But again, my guy started little and is still little; he's not losing like yours and my doctor has no concerns.