My pediatrician also pushed iron supplements from a very early age. I declined all supplementation (except vitamin D). Starting at 8 months my son began to eat meat and beans.
At 12 months, he got tested for hemoglobin/iron levels, and he was normal!
I declined the iron based on the research that I did. Babies have enough iron to last AT LEAST 6 months, and beyond. By the time their iron stores begin to taper off, as long as the baby is consuming iron-rich foods, then there is no cause for concern.
If your baby is NOT consuming iron-rich foods by 9-12 months (just my estimation), or seems otherwise lethargic, then perhaps you should consider getting her tested, or supplementing.