Does anyone know whether universal queue automata have ever been considered, and, as for Universal Turing Machines, some "small" universal queue automata are known?
Well, a very similar concept, called Tagsystems is an early universal model developed by Post. Here is the description from wikipedia:
A tag system is a deterministic computational model published by Emil Leon Post in 1943 as a simple form of a Post canonical system. A tag system may also be viewed as an abstract machine, called a Post tag machine (not to be confused with Post-Turing machines)—briefly, a finite state machine whose only tape is a FIFO queue of unbounded length, such that in each transition the machine reads the symbol at the head of the queue, deletes a constant number of symbols from the head, and appends to the tail a symbol-string that depends solely on the first symbol read in this transition.
It is explained in the introductory part of a paper by Woods and Neary for FOCS 2006 that small universal TM's are actually built from small universal Tag-systems. Hence there is a big competition in finding small Tag-systems.