I really would advise you to leave her in the main tank. You look like you have plenty of plants in your tank, so some fry will be good at hiding and won't get eaten (guppies aren't voracious fry eaters anyway).
Breeder boxes/nets are really too small for the mother fish to feel comfortable and may stress her out to the point where she aborts the fry, and they're too small for the fry to grow properly.
Guppies are the rabbits of the fish world (actually, they're much worse than rabbits!); unless you have multiple tanks for growing on fry, you cannot keep or save them all, so it's really best to leave them alone to get on with it.
Bear in mind that each female can have 30 or 40 fry (or more; I've heard of 70 fry in a brood!), every 30 days, and those fry can start producing fry themselves at three or four months old, so you could end up overrun in a very short time.
Leaving the mothers in the main tank will, hopefully, mean that you end up with a manageable amount making it to maturity.
I know it might sound harsh, but the very reason livebearers have so many fry in the first place is that, in the wild, so many of them get eaten.