We investigate the dust structure of gravitationally unstable disks undergoing mass accretion from the envelope envisioning the application to Class 0/I young stellar objects (YSOs) We find that the dust disk quickly settles into a steady state and that, compared to a disk with interstellar medium (ISM) dust-to-gas mass ratio and micron-sized dust, the dust mass in the steady-state decreases by a factor of 1/2 to 1/3, and the dust thermal emission decreases by a factor of 1/3 to 1/5. The latter decrease is caused by dust depletion and opacity decrease owing to dust growth. Our results suggest that the masses of gravitationally unstable disks in the Class 0/I YSOs are underestimated by a factor of 1/3 to 1/5 when calculated from the dust thermal emission assuming an ISM dust-to-gas mass ratio and micron-sized dust opacity, and that a larger fraction of disks in Class 0/I YSOs is gravitationally unstable than was previously believed. We also investigate the orbital radius $r_{rm P}$ within which planetesimals form via coagulation of porous dust aggregates and show that $r_{rm P}$ becomes $sim 20$ AU for a gravitationally unstable disk around a solar mass star. Because $r_{rm P}$ increases as the gas surface density increases and a gravitationally unstable disk has a maximum gas surface density, $r_{rm P}sim 20$ AU is the theoretical maximum radius. We suggest that planetesimals formation in the Class 0/I phase is preferable to that in the Class II phase because large gas surface density is expected and large amount of dust is supplied by envelope-to-disk accretion.
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