But just as its self gravity needs to be a certain limit to form a sphere, the same may be true to form a low density body, until the mass is sufficient to hold low mass molecules like He and H2.
It's a fucking nightmare to calculate such stuff. I could have done when I studied this shit in the 70's, but now all I have to go on is my old experience with this stuff, plus the fact that of the many thousands of objects we've studied zero of the low density objects are small. In fact, they are all very large. Most of them, by a huge factor, are stars!
So, I suggest that nature just doesn't make planet sized low density objects short of the mass of gas giants or above. (Unless there's some very small objects, of which there may be many -- an astronaut loses a Big Mac package on a space walk... 
just joking.)
The lowest density objects known are red giant stars, probably the best known, and largest of which is Alpha Orionis -- Betelgeuse. It's one honking big star, but its density must be very low.
In other words, if you want low density you almost have to have either very low mass or high mass. There may not be stable solutions in between.
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