Cooking fishcakes for 1 year old---how to hold shape AND get soft juicy texture?
In my experience cooking for small children I've found that just because they like a set of ingredients doesn't mean they will like them combined if the texture changes. I child who likes chicken and vegetables won't necessarily like chicken stew. A child who likes fish won't necessarily like a fishcake as the fishcake has a very different texture. 

That being said it could be that the particular type of fishcake you are making isn't to your child's taste. I think the reason is the breadcrumbs. Breadcrumbs are a good binding agent for ingredients that have lots of moisture and fat to release during cooking - as the mix cooks the breadcrumbs soak up the moisture and keep the mix together and retains some of the moisture. Fish and shellfish are pretty lean to begin with, and as they are usually pre-cooked when making fishcakes they will have already lost most of their moisture. If you use breadcrumbs to bind the mix there will not be enough moisture to wet them. You could add a bit of water but then you're going to get a soggy mess. 

I would suggest making fishcakes with mashed potato instead of breadcrumbs as a binder. The potatoes are naturally moist and hold things together well. I typically use a 60-40 ratio of fish to potatoes by weight. You can coat the outside of the patty with breadcrumbs when frying them off to give the surface some crunch.