Moving them will be fine. It's been done many times before. Just be sure to take time to acclimate them. Longer then it would take for adult fish, because fry are more sensitive.
Feeding them fry food for the first few weeks will be best for them...Hikari First Bites, or TetraMin Fryfood. Baby Brine Shrimp are also good. Once they are a bit older, and their mouths are bigger, you can move on to finely crushed flakes, and Frozen or Freeze-dried Brine Shrimp, Bloodworms, Daphnia...etc. Just make sure it is small enough for them to eat. BBS is also good through this. Try to feed them at least 3 times a day, too. Fry's stomachs cannot hold as much as the adults, and they empty faster.
If they are going to be in a fry tank, I would recommend a sponge filter, so they do not get sucked up. Or, if you have to have a HOB, you can put a breeder net over the intake valve. Be sure to keep the tank very clean, because fry need good water quality. You can make a little siphon out of airline tubing, so you don't suck them up. Or use a turkey baster. Just check one more time for any fry before you dump the water out. And always remember to use Decholorinator!
Good luck with the babies!