hi vix,congratulations on the eggs!!!!!
what i did when my peppers laid eggs was to remove the eggs carefully to a smaller bare bottomed tank & place an airstone directly under them to stop fungus forming.you do not need a filter for atleast 4 weeks.peppers are renouned for eating there own eggs,also if they hatch in your main tank your peppers & guppies will see the cory fry as food & eat them as there really tiny.
the eggs take about 5 days to hatch & the fry do not need feeding for about 3 days as they live off the yolk sack under there belly.you can then feed them a liquid fry food sparingly for a few days then move upgradualy to a powdered fry food.or i feed mine microworms (which they love),people also feed them baby brine shrimp but make sure theres no shells etc in with them.
you have to do daily water changes (i do 20%) & keep the bottom of the tank as clean as possible.i remove all uneaten food (except for microworms which can live for upto 24hrs in water) about half hour after feeding.if uneaten food is left in the tank for too long it could cause bad bacteria to form which will harm the fry.
wait to you see how tiny the fry are,there alot smaller than the guppy fry your use to!!oh yeah,one last thing...dont put the cory fry in with any other sort of fry as guppy fry etc will attack & eat cory fry.its happened to quite a few people on here before.
good luck with the eggs & let us know how it all goes.dont hesitate to ask any more quetions.
shaz