Congrats on the platys! I am by no means an expert, but when my platy had babies I left her in the main tank with the and some floating moss. In my case I used hornwurt but java moss would work fine too. After the fry are born, try to catch them and but them in the fry tank. I used a turkey baster to suck them up and put them in. I will tell you I had about 30 in my first batch, and it took me 30-45 minutes to get them all and transfer them. It was totally worth it though watching them grow up!
What size are the tanks?