Can eating ice sometimes be an indication of low iron?

My 2 year old is fascinated with ice right now. She opens the drawer to get in the ice bin at least once an hour and has started throwing tantrums if she can't get any ice. I made an appointment for her iron levels to be checked because my mother has had issues with iron her whole life and I myself had iron issues when I was my daughter's age. My mother-in-law thinks I'm nuts for getting her an appointment and now I'm wondering if I should just cancel the appointment because my MIL has made me feel like I'm crazy for making an appointment because of my daughter's sudden obsession over ice and having heard eating ice can indicate low iron for years.

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