In the case of the term 'rice plate' plate does not refer to an actual 'plate' but a type of meal equivalent to 'rice dish' which again does not specify the object the rice is served on but that it is a type of meal. 'plate of rice' specifies an acutal plate similar to a bowl of rice or a spoonfull of rice.
I am not sure how to express a 'rice dish/plate' in vietnamese. Maybe "ăn cơm cơm"? Probably not.
Rice plate can also be interpreted as Natt does, in which rice describes function. It is a plate for serving rice. But I think your use is the one I addressed above.
You can use gọi món (kêu món is commonly used in Southern Vietnamese) to refer to the action of ordering food although typically if you want to order you would use gọi món. "Cho tôi gọi món" is used to mean "I wish to order" even though the word for word translation is "permit/allow/let me (to) order food".