What is the best way to solve this? I could add an enumerated "type" field to the Unit class, but this feels wrong as it's polluting the model with data that it doesn't care about, but I really can't see any other way of doing this.
This is the way I would do it. The model should contain all important information, not only information you need for some calculations, but although data which are used to communicate important infos to the player, like a unit type (ah.. a goblin which seems to be quite weak).
Even a model name would be ok, all other model related data, like textures, mesh, animation description etc. are then included in view/controller.