I find this very interesting. While my son was on the same trajectory as your daughter in terms of the weight percentiles (or perhaps lower) - he started out really great, like your daughter, but continued to decline through 1 year. The doctors never told me they wanted to do any tests. Now there are more factors involved like he drank plenty of fluids, and I felt like I was getting the right amont of milk in him, but I was breastfeeding, so it's hard to say.
Soon as he started drinking cow milk and eating more food, he put on weight. Now, at his 18 month appointment he was at 100% for weight. I think at one point he bottomed out at 14%. I was extremely diligent about feeding him - anything he would eat. I make everything from scratch, and if he didn't eat one thing, I put something else in front of him until he ate a good meal. (Which was painful and frustrating for me at times because I work full time too.) It's only now that he is at 100% I let him go without eating much at a meal, and he makes up for it at the next.
Anyway everything turned out fine, but like I say, we thought he was getting the recommended amount of fluids. Also his head growth and height continued to steadily stay above average, even when his weight was down. So I am not sure - are ALL her measurements going down in percentiles?
On the one hand, you want to make sure she is nutritionally sound - there can be devistating consequences to not having the nutrition she needs. I believe that if you give them food they like, they will eat it. Maybe she isn't getting the choices she wants? I am not sure. Or she may have some stomach issues and it would be good to knwo that early on rather than letting her suffer from a lack of nutrition. No matter what one person or another have experienced with THEIR child, it doesn't mean the same for yours. If you are not comfortable with your doctor, then go to another. I changed my pediatrician, and while it was hard to do, I don't regret it for a second.
Good luck.