Soil is way too wet. It doesn't need or want shitloads of water right now. You can gently stand her up and with a chopstick or something and tie it, or backfill a little soil around her to help her stay upright.
DON'T MIST IT. It's gonna damp off if you keep that stem where it meets the soil too moist. If that happens, it dead meat. It doesn't need fertilizer, just a little water and some full spectrum light. And make sure the light is something like a T-5 fluoressant or some other cool light. Keep it about 8" to 12" from the top of the seedling. Weak light or light to far away will create a stretchy leggy seedling that will fall over.