Oh boy!
I don't suppose you can swap out the three females for three identical males when your kid isn't looking, can you?
Kidding! Well, kinda...
Sorry to break the news, but nope, they won't self regulate at all, and if one female is gravid, there's a solid chance they're all carrying sperm packets from whichever male(s) knocked up the one you can see carrying eggs...
And it doesn't stop with one batch of babies - each female can have several hundred fry, every month, even without a male around...
Female livebearers can store sperm packets and use them to self-fertilise when they're ready, and they can store these packets for even up to a year, so you could have many fry in your future!
Even from the one batch of fry, within a few short months you'll need to separate out the males from the females, because the young males from that batch of fry will quickly mate with every female they can, include the original adult females, so you can imagine how rapidly you go from one (or three) female(s) popping out fry every month, to many females popping out fry... Just to make it harder, all of the fry will look like females for quite a long time. It takes a while for the males gonopodium (anal fin/sexual organ) in males to develop, and by the time it does, they're getting ready to mate).
Now that I've scared you with the worst case scenarios!
Platies don't seem to quite as prolific as guppies fortunately, and it's more common for females to have smaller batches for their first batches of fry, and 20-30 for later batches. It's not super common for them to have hundreds in one go. But it can certainly still get out of hand pretty quickly. It's a lot of fun for a kid to see livebearers breeding, since the fry are born much more developed than an egg-laying fish, and grow rapidly, so it's a great teaching tool. And the baby fish are adorable! But you'll want to be making plans for how to manage it now, before the population explodes beyond your abilities to manage it.
The more plants and hiding spaces there are for fry, and the more well fed the adults are, the more fry are likely to avoid being eaten. But you'll still want the live plants, since they help provide decent water quality, and make all of the fish feel safer and more secure. The more fish in the tank, the more pee and poop in there, and the plants really help manage that. You'll want to monitor the water conditions though, and increasing water changes is best when you have fry, not only because of higher levels of ammonia being produced, but it improves growth with fry.
If numbers of fry are getting out of control, leaving the adults hungry for a few days can help resolve that issue, but only when the fry are a few days old and small enough for an adults mouth... and not many of us have the stomach to use that self-regulating method!
Talk with your local fish stores about whether they'd be willing to take the young once they're large enough. Most large chain stores won't - for fears of bringing disease into their store tanks. But privately owned fish stores are more likely to agree, and it's much easier to bag up the whole batch to take to a LFS than to sell off a few babies at a time via gumtree or similar.
Your size tank and stocking, you should be fine for the first batch or two, while they're young, but a separate nursery tank is a good idea, at least to be able to separate out the males away from the girls, and likely to raise future batches if you find yourself getting over run.
Good luck! Happy to answer any follow up questions you have
