What do you want to examine with the AC analysis? AC analysis is for determining the AC transfer characteristics of a circuit. If that's what you want, you can add an AC voltage source in series with the crystal.
If you want to see the circuit oscillate, then you need to use the Transient Analysis, not AC analysis. But note that it can be difficult to see oscillation in a simulation due to the high Q of a crystal and lack of normal circuit noise to start the oscillation. Sometimes placing an AC source in series with the crystal and having it generate a single short pulse at the start of the simulation can help start the oscillations.
An LED with no series resistor is a very low impedance and will tend to short the output.