Hi J.. I'm one of the women who responded to you originally. I recommended almond milk and am a die hard believer in not too much soy. Like I said, you can't avoid it and it does have its benefits but it should be limited in women - esp those who are young or reaching puberty, those who are menopausal and those with estrogen responsive cancer. Funny thing, we are the only country that doesn't ferment their soy milk. All other countries do and that fermented form does not have the same properties (estrogen imotating) as non-fermented does.
Anyhow, as far as I know almond milk is perfectly fine to give to young chilren. My neice who's lactose intolerant has been drinking it since she was itty bitty. I like the one you can get from Trader Joes, it's not sweetend and vanilla flavored. It's as close to milk as you can get as far as sugar and calories is concerned. Plus spend a little time researching the benefits of almonds. They are very high in antioxidants and many valuable nutrients. Unfortunatley, rice and rice milk can't say the same. So she would be getting a healthful drink, chocked full of nutrients, low in fat and sugar and obviously better for her than cow's milk.
BTW - I applaud you for being your daughter's advocate. Doctors are said to PRACTICE medicine for a reason. Remember, you know your child better than anyone and I'm so happy to see you're following your instinct. I have met so many parents that do whatever they're told "because the doctor said so" even if their instinct was telling them something different. I'm not saying doctors can't be trusted or know nothing. I'm just saying they don't always get it right every time. Best wishes you and your little one!