What ship? The Dream has Vanellope's:
I don't know if they have other options like sherbets, etc. I believe I've seen sherbet in the MDRs (not on the menu, but can be asked for).
No other "novelties" type ice cream foods, only cones. And Mickey bars.
Sorbet is (usually) non-dairy. Sherbet, however, contains dairy. I've seen rainbow sherbet available in the dining rooms featured in the sundae on one of the menus. I've requested just a dish of the rainbow sherbet on those occasions.
I've seen sorbet available in Palo as well.
ETA: If this is for a dairy allergy, perhaps if you contact ahead of time as a special dietary need they could stock a non-dairy frozen dessert like Tofutti or Rice Dream or something like that. Pure conjecture on my part; I've got no personal experience with special dietary accommodations.
My son is lactose intolerant and our head server brought him sorbet every night for dessert. He had raspberry or mango. But we planned his meals with her the night before and I let them know ahead of time about his allergy.
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