It was about that age that I made the switch to adult stuff for my daughter. Her hair just always kinda looked messy and not very clean (I was using Suave as well) even though I'm sure it was, it just didn't look that great. I went through a few things with my kids but I have settled on one I really like. To be honest, the biggest difference I've noticed in the kids' hair and my hair is when I used shampoo without phalates, etc. It truly has made the biggest difference. I can't even remember the name of the one I use now, it comes in a round, red bottle, but I've also used one from Costco that is free of junk and it works well too. It is the Kirkland brand. I get the red one at Bed, Bath and Beyond and although it's a little pricey, it's worth it to me. Plus, you can use the 20% off coupons.
I haven't had a problem with using non tear free stuff on the kids. I thought I might, but really it isn't an issue. My son basically started using the stuff at age 1-1.5 because I got tired of buying separate stuff for them. Just help her rinse it out and I think it will be fine.