Personal pet peeve so I apologize in advance.
Someone has to be <5% or there couldn't be 100% !! It doesn't mean she's abnormal. It COULD mean there is a problem, particularly if she started at 75% and dropped to 5%. If she has always been petite it is not so much of a concern. Especially at 1 year of age- she is getting more active and burning more calories.
You say she has always been petite... were your or your husband small? Is your other child small? Are there small people in the family? My husband and I were both small and now we have small kids... it makes sense.
I also take issue with doctors telling people to fatten up kids. If an adult ate a Big Mac every day she would gain weight but that wouldn't make her any healthier. If you add things that are high in fat- like whole milk, oil, etc you are not increasing her nutritional status (of course some fats are better for us than others but none of them are GOOD for us, just less bad). If she had a health problem the concern would be with her getting adequate nutrition- adding fats will not take care of that problem. It will make her gain weight and set her up for a lifetime of unhealthy eating, weight problems, diabetes, heart problems, etc. It will also mask the problem if she in fact has an issue.
If you were feeding her a really healthy diet and she was showing sign of malnutrition, unhealthy hair or skin, etc then I would be concerned.
So to sum it up, I received this advice from one doctor and promptly found another doctor who was more informed and less worried about covering his butt with expensive and yes, invasive, testing.