So in a real sense, the DNA contains the blueprint for the machinery to copy the DNA itself, but not the instructions for building that machine from the blueprint, the same way a software quine doesn't necessarily include the source code for a compiler.
Definitely a definitional problem, but that's my shot at resolving it a bit.
Then again, DNA polymerase is not perfect, and DNA is not immune to single nucleotide changes having a real effect, so it's only a quine in the "spherical cow" way of looking at it anyway. But it's certainly the most "quinish" thing in nature that I can think of.
But I may have been a bit unclear about my mapping of computer and biology terminology to this question.
I tend to think of a computer programs as being mathematical machines, and proteins as being molecular/chemical machines. Motor proteins "walking" along microtubules is the most vivid example of this.
I'm sort of torn between both worlds here, honestly. I like both perspectives. Viruses especially have a very quinish quality to them in that they're stripped down to just enough stuff to get a host cell to make more viruses.
