Maybe I can help show how it all depends on the doctor.
My daughter was 8 lbs and 13 oz when she was born. A nice plump baby at birth, but slimmed down as she grew. At 4 months the doc started asking if she was eating as much as she wanted. My daughter was in the 25-30% in weight & height. She was growing consistently and, yes, she ate as often as she wanted since I didn't believe in making newborns wait until I was ready to eat. She was breastfed and drank formula as well. My doctor said she should have doubled her weight by 4 months. That's the "standard" they look for. This meant that instead of 12 lbs she should have weighed 18 lbs at 4 months, which means she was supposed to weigh in at 22.5 lbs at 6 months if she continued to gain weight at that rate. I explained that I was a very thin until age 20, as were all of my aunts, mom, and sisters, and that was with me out-eating my dad 2 plates-to-one at the dinner table (I weighed 103 at graduation because I was always bicycling, skating, running, etc.), my husband was put on a malted milkshake high-calorie diet in middle school because he had such a hard time gaining weight, and his sister was a very petite thing as well all of her life. The doctor finally stopped asking once she started to eat solids and I would always have a list of the things my daughter loved. She didn't weigh in at 22 lbs until almost 2 years old and I think she was supposed to weigh about 30. If I remember correctly, they want the kids to weigh about 10 lbs per year of age, until they reach about 3. Then they start talking about how they shouldn't be so overweight. My son is 5 (will be April 30) and weighs 34 lbs, my daughter is 8 1/2 and weighs 54 lbs. Yes, they look thin (can't count their ribs) so people ask how I keep the weight off of them. I don't. My kids don't sit around eating all of the time, but I don't have a problem giving them donuts and stuff. They don't sit around playing video games or watching tv all of the time, but we do have our video game/ movie marathon lazy weekends. We have family game night. We read together. I don't have them constantly exercizing, but they love to run, jump and play. They play on the swingset, they play tag, they jump on the neighbors' trampoline, they ride their bikes, they rollerskate.
I know doctors and fitness enthusiasts don't like to hear it, but somepeople are built thin and others are heavy (like I am now - changing my eating habits, the walking and biking is helping me though).
Your daughter's 6 months old. If her weight begins to make life difficult for her, such as she can't discover her toes or she can't turn herself over, then yes there may be a problem. But if she's reaching those milestones at a good average pace for her, then give her time to get walking and then see how much baby fat she wears off.
My friend's baby is a big baby. Her doctor was telling her what your's is telling you. She weighed less than my daughter at birth, but weighed in at about 20 lbs at 4 months. I could barely carry her for long. She is 8 months old now and is 30" tall (she is up to her Mom's mid-thigh!). Her Mom is just about 6' tall. So that probably has a lot to do with it. Not sure on her weight since they live in Missouri now. However, at 8 months she is cruising the furniture. My daughter didn't do that until 11 months!
Give your daughter time. That's my advice.