Looking further into the possibility that this object is an extinct comet nucleus, I find it's not likely, after all. A combination of orbital factors called the Tisserand parameter is often used to distinguish a comet from an asteroid. Comets typically have values of less than 3, asteroids greater than 3. 1998 QE2 has a Tisserand parameter of 3.24.
I looked at a list of nearly 500 short period comets, with orbits likely to resemble that of 1998 QE2. Only a dozen had Tisserand parameters above 3. The highest value, in a single instance, was 3.212.

I was wondering what had been determined spectroscopically about the mineral composition of 1998 QE2. Inquired about this to Alessondra Springmann, an astrophysicist working on this object. In her prompt reply, she indicated that no definite classification had been settled on, but it appeared that the object had characteristics of class X and class D asteroids. Class D asteroids are essentially metallic objects. Class X are made of mixed silicates, carbon compounds, and possibly water ice. An interesting combination of very different sorts of objects.

The average density of class D asteroids is about 9.6 g/cm^3, that of class X, around 2.9. It seems odd that an object believed to have a density of approximately 1g/cm^3, as determined by dynamical methods, should seem to be made up of materials, that, if mixed, could give a density of 6 or 7. It appears that, though it departed from the vicinity of Earth over a month ago, 1998 QE2 still holds some surprises for us.

Odd, that in an object that was said to be 'primitive'-- that is-- apparently largely undisturbed since its origin, should appear to have features suggesting that it is the result of the complete mergence of two very different sorts of objects. One is metallic, and the other made of silicates, carbon, and possibly ice. They appear to coexist now in one, basically spherical body. There is apparently no established class of asteroids that combines these features.

Erratum to my July 3rd post--The first sentence should read: "The average density of class D asteroids is about about 2.9 g/cm^3, that of class X around 9.6." The figures were inadvertently reversed.

There seems to be yet another layer of complexity to the mineral composition of 1998 QE2. Astrophysicist Alessondra Springmann reported an apparent classification of an odd combination of the very dissimilar classes X and D. Dense metallic and lighter mixed silicate types, respectively.
Spectra taken with the Hale 5 meter telescope at Palomar observatory give a 'best fit' for class C, similar to carbonaceous chondrite meteorites. Ms. Springmann, in response to my follow-up question, suggests that different sides of the object may be of these different compositions, thus explaining the seemingly contradictory results.
If this turns out to be the correct explanation, this object will presumably have an asterisk after its taxonomic type, in the asteroid lists, and a bottom-of-the-page note, indicating its peculiarly mixed and partitioned makeup.

It almost looks as if a class C asteroid received debris on one side, from the nearby collision of a D and an X class asteroid. Odd, though, that the debris didn't persist long enough to coat both sides of the object. It only takes a couple of hours to turn its opposite face in any given direction. Has anyone a better explanation?

There have been 15 years of observations of 1998 QE2. It has been consistently classified as a class C asteroid, similar to carbonaceous chondrite meteorites. Odd that recent observations suggest that one side or portion of the object has mixed spectra of D and X class, mainly silicates, and metals, respectively. Why had this not been noticed before? If these features are inconspicuous, and could only be detected when QE2 was nearby, why did the overall C class spectrum still not predominate, or at least figure prominently in the spectrum?

Dr. Marina Brozovic, head of JPL radar investigations into 1998 QE2 stated that it was not expected that this object would have a moon. Most near-Earth asteroids with moons have rotation periods of around 2 to 3 hours. With a currently estimated spin of about 4 hours, this object appears to be exceptional.

It's been six and a half weeks since 1998 QE2 passed nearest Earth. So far, we have been shown no firm determination of the density of the asteroid or its moon. We have only a 'very preliminary' figure of ~ 1 g /cm^3 for the primary.
Even that had to be specifically asked for. It had not, and has never since then, been offered on likely online sources, as far as I can determine.
One wonders what has become of a firmer, better defined figure. This was supposed to be readily attainable with mathematics known for centuries. My inquiry to JPL about this has gone unanswered.