It sounds like your system is all digital except the DAC output. Most of the time, I advise against using separate grounds, especially if passing radiated emissions testing is a concern. Personally, I would not have two different ground planes. It would be OK to have two ground planes and connect them together with lots of GND vias.
But it is a very good idea to study the placement of components and the routing of traces to make sure digital signals and digital return currents on the GND plane are kept away from sensitive analog signals. In your case, you need to focus on the voltage reference for the DAC and the DAC output itself. Those are the two places noise would be most likely to cause problems. Review any documents that provide guidelines for filtering DAC reference voltage inputs.
Generally, make sure the digital systems are well designed, with bypass caps and so-on.
Just for the sake of filling out the answer, the most sensitive signals are microphone signals. Traces must be routed with extreme care. Line level signals can also be pretty sensitive, especially if it is line-in and you are feeding the signal to any type of amplifier with high gain and/or high input impedance.
Headphone outputs are usually not very sensitive. Speaker outputs are fairly immune to low level noise. If you have problems with headphone or speaker outputs, the problem was probably created at the input side.