She (and the fry) would be far, far better off left in the main tank. Breeding traps are too small for the females to feel secure which leads to stress, which can cause them to abort their fry, or succumb to stress related diseases, like fungus and whitespot, and they're also too small for the fry to grow properly, leading to stunted fish.
I know it might sound harsh, but you cannot keep every single fry if you have livebearers; unless you have a large amount of spare tanks for growing on, you'll just end up with masses of stunted, unwanted fish.
Your tank looks like it has plenty of plant cover, so some fry (hopefully an manageable amount) will survive.