I've used many things to carry my eggs. I've bought baskets, I've made baskets, I've carried them with my hands, and lots of other things. After all these years, these are my favourites. The first option and the more accessible one is, a plastic bag! When I go to open the chickens I bring it with me and hang it on a nearby tree. Once I've gathered all of my eggs for the day, I place them in the bag. The good thing with a plastic bag is that there isn't any excess room for the eggs to break by rolling against eachother, the only downside is that the bag does not protect them if you accidentally drop them, or if they hit something. My other favourite is a smaller bucket. That might be a better case for you, since a smaller bucket still won't have room for the eggs to break, and will provide support if you accidentally hit something. Another option you might want to try is a wooden basket. My recommendations, a wooden basket made from softer wood, and the basket shouldn't have any corners, I've found they don't break as easily that way