I'm not much taller than your daughter and even my BMI isn't 89 and I weigh a hundred pounds more (I'm 5'9" & 254lbs with a 37.5 BMI). I think the doctor did not measure her right at all. Plus she still has some years before she is fully grown and her metabolism changes to reflect that.
At her age, you need to be careful how you address the issue. The focus needs to be on healthy and not how she looks or weighs. Her diet needs to focus on putting healthy food in and don't police the amounts of it. She just needs to keep active and exercise in ways that are fun and encourage fitness without focus on losing weight. Doing it together can be fun and won't seem like you think she's fat or ugly in any way.
Eating disorders suck which is part of my problem now. I had people calling me fat in high school which lead to anorexia and then bulimia when people noticed how little I was eating. I managed to get things better when I was pregnant with my son as I wanted to focus on giving him a healthy mom during and after my son was born. I was doing great for years until my son's mental health got really bad and I was pregnant with my daughter. I could barely keep down anything and was on bedrest. The really healthy meals I used to cook got were pushed aside for convenience. Then I got into eating when I was stressed especially junk comfort foods from there since I couldn't do anything on bedrest and my weight from constantly throwing up was a big concern.
Once the baby was born in the NICU and my husband and my son had different major mental issues bubble up at the same time and I just gave up on caring that the food was mostly junk or not having enough time to focus on myself. It wasn't until this past year I could and had to focus on myself again. By then I realized I had gained an extra 50lbs since my daughter was born and hadn't lost any of the baby weight. Now I'm struggling to lose the weight in a healthy manner, not relapse into my anorexic or bulimic tendencies, and still love myself extra pounds and all. Once you have food issues and an eating disorder everything is so much harder.