The vowel change following [q] is a tough thing to get a good grasp of. It might be the best to just try to pronounce as written (not as the IPA instructs), but relaxed and natural, not pushing for the "correct" intonation. I'm not sure, but I think my vowels do shift at least some if I just let them.
Do Peterson's vowels shift after the [q] on the audio examples? I can't say.
It might be also worth noting, that the dothraki use only four phonemic vowels. Finns have eight. English have, I don't know, many. Seems to me that the dothraki might all in all pronounce vowels more loosely than most of us do.
Kh is actually another example of a phoneme with at least some range of different ...phones... allophones? I think David has said it sometimes shifts to palatal fricative. There aren't many phonemes nearby, so kh has space to wiggle. Listening to David (the latter relay) there seems to be two, maybe three different ways he says it. At the start of a word (kher) there is a bit of an attack; the phone is not terribly far from kh the actors sometimes seem to fall into. At the start of a syllabe (lavakhok and lekhaan) there is maybe less attack, but the phone is still harsh (even with lekhaan, where kh isn't on stressed syllabe). At the end of a word (elzikh) the phone tends to be a lot softer, closer to h.
What would that make in IPA codes? You can pronounce the same phoneme softer and sharper, I think, so maybe they all are just [ x ]. Maybe they should be [ x ], but aren't really. Even Peterson's pronunciation might shift in live situation more than the language allows. [ x ] isn't a phoneme he would use that often. Maybe they vary as they should, between [ ç ] and [ x ], and maybe even visiting [ ɣ ] or [ ɰ ] for more emphasis.
