Glad to hear you are up for buying more tanks already and that your female had no problems with being caught and moved only hours before giving birth. They often give birth prematurely when moved.

If you can afford, or have the room for, two tanks then you will be able to get the breeding under some sort of control. The fry can be sexed as early as 3-4 weeks but often it is longer. It depends a lot on the growth rate which can be determined by water quality and temperature, types of food provided and frequency of feeding and also tank size.

The male fry may not develop their gonopodium for months so that is not a safe way to sex them. It is far better to look for the gravid spot on female fry and remove them to one of your new tanks (see all the info on cycling a new tank in the Immediate Help section). The males can be left in the first tank until they develop the gonpodium (which can occur overnight) and then moved to the 3rd new tank. This way you will have a tank of males, a tank of females and a tank for fry which can later be used for selective/controlled breeding. If you don't do this you will find yourself with hundreds of guppies within 6 months providing their water quality is good.

Guppies can store sperm for up to 6 months. They can produce fry from that stored sperm every 28 days. That means that even if you separate your male and female today, she could still keep having fry every 28 days for the next 6 months and some of those batches may well contain 30 fry. When you consider the rule of thumb, 1" of fish per US gallon of water........are you starting to chew your fingernails yet :)

I can't stress enough the importance of cycling a new tank. You don't mention what size your tank is. If it is a 45 litres or more then you may have no problems having added just 2 fish to start with but if it is much smaller you may. If you are not familiar with tank cycling, read up and then return and ask away.