I found an example "sketch" for a sam3s,
but I feel the code is instructive for the Due as well.
I do not expect this to run on a Due.
it shows the dac and adc being driven by a timer, and consuming/producing
arrays of data by using the PMC dma.
for me this solved how to run DAC and ADC in parallel.
just use the zip file, the separate pdf is the wrong one.
This can be done also on the Due but it is a bit touchy regarding hardware. You can be inspired by the SAM3S-EK schematics to reproduce the system on a proto shield.
As far as I know, SAM3X and SAM3S share a very similar ADC and DAC... ;-)