Here's how I wrap eggs for shipping
BubbleWrap comes off the roll in 12"x12" pieces. Cut in half for 2 6"x12" pieces.
Fold over the ends to make a pocket and tape it.
Place the egg in the pocket.
Fold the sides (like you're wrapping a burrito).
Tape it closed.
Put a good layer of 'cushioning' / 'filler' in the bottom of the box.
Line the box with big bubble (5/16") BubbleWrap.
and place the eggs inside.
Fold over the sides of the big bubble Bubble-wrap and tape it closed.
Fill in corners and gaps with more of whatever 'filler'/'cushioning' you have handy. On these boxes, 'filler' is pages from an old phone book (and Grace, those are your Frizz eggs). Crumpled newspaper, plastic grocery bags, shredded paper, air pillows, etc also work well.
Add more filler to cushion on top (there should be no empty space for the eggs to shift).
Tape it closed.
Weigh the box and go to USPS Postal Calculator to calculate the postage.
I ALWAYS ship eggs using Priority Mail with Delivery Confirmation.
Of the Flat Rate boxes available, the only two I consider suitable for shipping eggs are Medium Flat Rate Box / 11" x 8-1/2" x 5-1/2" for $10.70) or Large Flat Rate Box / 12" x 12" x 5-1/2" for $14.50.
A Priority Mail #07 Box / 12" x 12" x 8" is a good choice for shipping eggs and is often less expensive to ship than the smaller Med FRB1.
There is no way to know for certain without calculating a weight to a particular zip code.
You can order boxes, etc at no charge by going to The Postal Store.
I like to keep #07, Med FRB and Lrg FRB on hand "just in case".
Print the postage / shipping label (if using PayPal, there will be a instructions to pay and print postage from there or you can use the calculate postage link above).
Label it with 'Fragile', 'Perishable', or whatever you think is appropriate. And get them to the PO.