It can be based on the quality of algorithm used to drop the pitch. Digi's factory Pitch Shift plug in is faaar below the quality of number crunching compared to some of the higher quality (and more expensive) plug-ins like Serato Pitch 'N Time and Ableton Live's Pitch Shifter.
Another factor is sample rate - drastic changes to pitch or time can degrade sound quality to the extreme based on the above stated factor. To combat this, try using 192k on an HD system if you have access. As you know, the more samples = the higher definition for processing on input and allowing a higher definition output. Bit depth doesnt matter I wouldnt guess as its main purpose is in the dynamic range. A sampled frequency is a sampled frequency regardless of where it is on a scale from amplitude range. Quality is about # of samples.
Another option is to pitch the dog down only say half as much, and use a low end harmonic exciter/generator such as LoAir, LowEnder (I think thats what its called), or iZotope Ozone harmonic exciter to boost the low end material. If the low end is there originally, boost it - if it doesnt have much low end spectrum to start out with, use a subharmonic generator for supporting the sound.
Let me know how things work out!