In circuit theory, the definition of a short circuit is 0 V across its two terminals.
In your example, this would mean you are forcing an infinite current through the transformer's output (and, as a consequence, through the input, too), because the short is reflected to the primary side, and the network feeding the transformer will, theoretically, force an infinite current into the transformer.
In real life, the DC resistance of the copper windings (secondary and primary!) will prevent the universe from melting down, but your transformer might become too hot.
Now, the rating tells you what you can do with your transformer under proper conditions: Connect a load that doesn't take more than 1 A when being fed with 12 V. If your load uses less than 1 A at 12 V, you wil still get an output voltage of 12 V because the ratio of the windings defines the ratio of the voltages.
Real transformers take their losses into account and are designed for the rated voltage output at their rated current, so they will output a bit more than the rated voltage under no-load or light-load conditions.