As far as the height/weight gain, did he show you her "curve" that is plotted out with all her past measurements? It should look like a steadily curving line. As soon as it deviates and goes more sideways or straight up, that is when you should be concerned. As far as HOW concerned, I don't know.
Now for the head circumference I can tell you my experience. First- the reason they want to check her head is for fluid on the brain (hydrocephalus). My son has a gigantic head as well. My doctor wasn't overly concerned once she found out my husband has a larger than normal head. (Thank god I didn't know that in advance of delivery, I would have been panicking!) But she was monitoring, also on that curve scale. He was always >99 percentile for his head but usually in the 15-20 percentile for height and weight. His curve was not a curve at all- it was a straight line going up. It wasn't growing gradually like it should.
At six months she gave a couple of options- wait and see what his measurements were again at the 9 month check up, or go and have an ultrasound done while his soft spot was still open. She said that if we waited and it was still going straight up at 9 months he would have to have an MRI to check for fluid on the brain. I was also told that he would be under anesthesia but that it would conscious sedation like jenni said below. She said there are still risks and she would prefer to do the ultrasound. She also told us that it is important to diagnose it as early as possible to have the best chances of successful treatment.
Maybe your other children had large heads but their growth was at a normal rate with the nice correct curve, and your daughter's is going straight up like mine was? It might seem to you that it did not get bigger all of a sudden, but according to the charts it might have. I agree since the other kids have large heads that it is probably just a big heads running in the family thing. But the doctor has to let you know about possible issues, that is why we do well-baby visits. To make sure everything is progressing normally. They can't disregard abnormal numbers on a hunch that it is just a family trait. I can't honestly say I would go with the MRI either in your situation. But the doctor has to recommend it in case something IS wrong. I would go back and talk to him more specifically about hydrocephaly, what it's risks are, what the odds of him having it are, and what to expect if you do get an MRI and the risks associated with that. Get a lot more specific info to help you make your decision. Good luck!