Also, if you have one of those, you could let her give birth in the tank, and just scoop the babies out as you see them, and put them in there to grow them up. Just make sure you have plants and hiding places for the fry.
Not putting her in the net will also probably be better for her, because they can stress them out a lot, and maybe even cause them to abort fry. Fry tanks, or just letting them have birth in the tank is usually better for their well-being.