Hi celias90,
Your platy looks very pregnant to me, but it could be just her with her colours. I've bred both Guppies and Platies in the past and found the darker the spot in her stomach is and the fatter she is the closer to giving birth she is.
Platies and Guppies give birth usually once a month. I've always used a floating tank or birthing trap for my fish. I bought a female and male Platy at the pet shop and about two or three weeks later the patch in her stomach had gotten darker and she had gotten fat.
I hadn't planned on breeding them again, but my male was picking on her so I thought either way she'd be better off alone in a breeding trap and I did want babies again. Three days later I had nine babies, that was almost a month ago now and they're all alive and grown and still living in a breeding trap. You sound like you have a better setup then myself, though. With a tank that big, I wouldn't bother with the breeding trap or keeping the babies in a breeding trap, but if you want to make sure you keep all the babies, I'd setup another tank just for the babies with a sponge filter and some water plants. The key I've found to getting them to grow is keeping the water around 27 degrees Celsius. Lower temps seem to slow their growing and by the time they're old, they're still the size of a baby. Just remember, Platies can have many, many babies every month so don't worry if you lose some.