While it's true that female ghost shrimp will eat baby shrimp, if the tank they are in is a decent size and has sufficient plantings, or decor like wood and rocks for babies to hide in, there's a decent change of having babies survive. The larval stage only lasts 4-5 days. Timing is temperature dependent. They do better at temps around 72 or 74 or so.
If you do get babies, you'll see them hanging upside down at the water surface during the days and they sink out of sight in darkness, until they begin to swim. Takes another few days for that once they show up. You'll see tiny shells in the water, which are the moulted shells, usually not dead shrimp babies. I've raised a number of broods in tanks with fishes galore, but do better if there are no fish. If you put a pregnant shrimp into a small tank to try to get more babies to live, take her out after she lets her eggs go.
Eggs hatch after they float to the surface, and the larvae float freely for the few days they need to morph. If you can, feed new morphed babies micro worms or new hatched BBS. Once they are moving around on their own they eat anything they can find and don't need special feeding. Most of them love sinking pellets though and will argue over them, but they don't fight to harm each other.
A sponge filter makes both a good filter and a good food source for any shrimp.
Incidentally, palaemonetes are a native species to the southern US, and live in many inland waters. So they're quite hardy and surprisingly tolerant of water conditions that will not suit other shrimps. This is not to say you can let the water conditions get bad, but compared to, say, Crystal shrimp, they're well able to take some nitrates in their water. Levels up to 30 ppm will be tolerated, but I prefer to keep it at 20 or less.
Cherry shrimp are Asian and come from similar habitats, and are likely about as hardy as Ghosts. The nice thing is that they are 'high order' shrimp who have babies just like themselves. Ghosts are 'low order' and have larvae first. But there are many other shrimps who also have larvae such as the Amanos and many other Caridina species, and Machrobrachiums, which include our familiar cocktail or BBQ shrimp among their numbers.