C.P.
There are still some thicker training pants available - they worked great for us. I've seen Carter's at Target, Babies R Us, and online at babycenter.com. I also used the plastic covers to help contain accidents.
Carter's has a size 18 mo. that might work well for your petite daughter. I also bought some great ones and JC Penney, and Hanna Anderson sells some nice, but pricey organic cotton ones.