I think this is pretty normal, whether the eggs are large or not. I regularly boil bantum eggs. If your girls have just started laying, the egg size will gradually improve. There are lots of threads about peeling fresh eggs and the various tricks. I personally place my eggs gently into already boiling water, boil for 12-14 minutes, then ice bath. Aside from the occasional issue, I have found this to be very helpful in peeling fresh boiled eggs. Search it within this site, it is an often talked about issue, and lots of ideas from vinegar to salt in the water to help make it easier. Good luck.
Very fresh eggs are almost impossible to peel. I've tried all the tricks, but never found one that actually works. When we want hard-cooked eggs we put a carton in the back of the fridge for three weeks. Older eggs peel like a charm because they have larger air sacs and their membrane isn't held as tightly.
I found this trick accidentally , but it seems to work. After I hard boil the eggs and put them in an ice bath I dry them then put them in a large zip lock bag in the fridge. They peel like a charm the next day.
I've tried about every trick or tip I could find to help with this problem.I am now just boiling my eggs as usual,no matter how old they are.After I finish boiling I run just enough cold water on them to be able to handle them and start peeling.I usually crack the big end on the sink and them tap it around till it cracks up the sides.And I peel under warm running water.You have to get under that thick inner membrane.You can tell when you do as the cooked egg will feel very slick.I was having eggs that had layers of the white peel off and some that just tore to pieces as I tried to peel them.I make alot of pickled eggs and I always want perfect pretty peeled eggs for that.Out of the last 10 dozen or so I've done I've only had about 5-6 that didn't peel easy.Thats pretty good out of over 120 eggs.Oh and I have egger-easters and mixed large brown layers plus bantams.They all peel the same since I've been doing it this way.I hope this helps.
Fresh eggs are acidic to protect the potential chick from bacterial infection and encourages the shell to stick to the egg. You can either wait at least a week to boil them, or you can add salt or baking soda to the water when you boil them. The salt or baking soda lower the acidity in the egg and allows the shell to separate easily.
I read somewhere if you pressure boil them they will peel easier. I don't own a pressure cooker so I have not tried this. But as far as your eggs being tiny, Feed your girls some oats. That I did do, and it worked no more tiny eggs!