Aww, Aida, I'm sorry. The first thing that came to mind as a good supplement source for kids was Pediasure. (I love Ensure and because I'm dairy intolerant, it's the perfect drink for me since it uses soy (I think).) At least with Pediasure, you'll know your baby is getting vitamins in safe proportions. I haven't heard anything negative about Biotin but I would try diet and Pediasure first, and then talk to your doctor about biotin. For diet, here's a hair-enhancing diet
I once posted. Even if you cannot adhere to it strictly, it won't hurt to try it once in a while. And then just make sure your baby is getting a well balanced diet. If you can find a flavor of Pediasure that she likes then you can make that a between-the-meals shake or TV-time treat.
While you wait on the hair to grow, perhaps people with healthy TWAs here on LHCF can recommend good oils/moisturizers that don't have harsh chemicals that give hair a nice, healthy glow and soft feel. You can then bring that out of the TWA your baby has and sing praises about the softness and shine till she begins to feel that hot about herself. She might start to appreciate her hair's healthy state so much and love it, she'll forget that length was ever an issue. Tell her you two are gonna work on making her hair da bomb. Perhaps you can put a plastic cap on her head with a nice oil/conditioner on for an hour before you wash it. And then perhaps a serum after the final rinse while wet, then apply moisturizer then comb it. Serum makes hair feel smooth and look shiny. Praise the shine, the softness...and not just then, every time you look at her, rave about it, even if she was thinking about hair. This may be a blessing in disguise because you're gonna strengthen/beautify her hair right from scratch and use the right care on it so that she'll have a mane that's the envy of town. So when she joins LHCF in her later years she can post on that thread about myths from moms, "My mom could kick butt when it came to caring for hair."
A little psychology goes a long way. Let her not know that the diet or drink are for hair. Take the attention off its growing long, and focus on making it the coolest hair around. And while you'll secretly be working on growing it dietwise, she'll be showing off her natural glorious crown having forgotten length mattered at all. When it's long enough for cornrows, find someone who braids kids to do some out-of-this-world designs on her, and buy her cute adornments. I like braids meeting at the top of the head (like a pony tail) and you can use different adornments where they meet. Or have them meet on one side of the head where people make partings, only imagine the meeting part going all the way back so parallel cornrows meet there and their ends are joined in some fancy way like with a raised French braid going back. I never had long hair as a kid but I was the envy of town with my cute li'l cornrow styles. Length never crossed my mind.
Wishing you both happiness...