Getting some killifish eggs, hatching them and raising the fry can be an amazing experience.
Your eggs were packed in peat moss because there is a feeling that they travel better that way. You didn't mention what species you ordered, nor how many eggs were sent, nor when those eggs were laid or at least collected. Neither did you mention if they were "plant spawning" killies or "annuals".
There are over 800 killie species that have been described. Many of those are available from time to time and there are many slightly different strains from different collecting localities. Some are easier to care for and reproduce than guppies. Others are pretty challenging.
If this is an Aquabid item, would it be an invasion of your privacy to ask what bid was it?
About what temperature will you keep them at?
Do you know roughly what your water supply's hardness and/or TDS (total dissolved solids) would be? (I use a TDS meter - a.k.a. the poor man's hardness meter - a lot because I have our towns most recent water report and can factor how much there is of everything from the TDS total.)
Would you please edit your question and mention as many of those as you can. More advice can be offered.
If you've some pretty clean aquarium water, I would use that with the eggs now! You import a little something towards a nitrogen cycle that way. After six days I would bring in new aquarium water again, maybe just after a partial water change in your tank.
It is better to keep the eggs in a dimly lit place. That is especially true of killies from tropical rain forests. (I have lost eggs picked and absent-minded left a day in a well lit fishroom.) Desert pupfish on the other hand,
can be left in a fairly bright room the two weeks it takes them to develop and hatch.
Low light plants or fast growers with them after they hatch are both terrific. We don't want snails around eggs, but small ramshorns around fry are usually a good thing.
The most dangerous disease for killie fry is velvet. As with Ich, and even fish TB, there may commonly be a few velvet organisms in the water. Rotting bbs (baby brine shrimp) provides a perfect environment for a velvet explosion. Snails clean up uneaten bbs.
That danger is also why I would be very cautious using frozen bbs or, without a current from an airstone, even eggs that had had the shell removed (decapsulated bs eggs).
Hatching live bbs is expensive because of the cost of eggs. I will check around for "good" deals. You might look at the brineshrimpdirect site for ideas on hatching a tiny amount at a time.
It isn't always legal to keep open water containers in some towns. But newly hatched mosquito larvae can be used without endangering others or one's relationships with family. Take a look at my article on mosquitoes in sources.
Some killies, like the gardneri group, will take finely crumbled flake food. Snails are still needed for clean up. And it is wise to remember that variety in foods is always good.Killifish are usually kept in a species only tanks. But you could start 1-30 fry in a plastic shoe box or a 1/3 full 5-gallon tank.
I wouldn't worry about keeping them with peat moss. It may be beneficial, but a wad of Java moss is vastly superior company for fry and cleaning is easier.
The last source below lists incubation times for Nothobranchius eggs. I'm guessing that you might have them. Times accelerate with higher temperatures and humidity levels. The knock on a couple of Thai sellers is that they seem to send the eggs later in that period. There are several stages that annual eggs go through. Early eggs are more hardy.
Mailing seems to accelerate hatching the time. If your eggs arrive and they are near the end of that incubation window, put them in water very soon. If & when they hatch, gradually get the peat out of the water.
One can wet eggs that don't hatch, re-dry them on a paper towel & try a couple of weeks later. If they are too far into their incubation cycle none many hatch.
All the best!