Dogs lack the facial musculature that humans have, particularly in the lips and tongue. Plus they cannot control their breathing to the degree humans can. Things like their open cheeks, longer oral & nasal cavities, and vocal fold anatomy (including placement) hamper their ability to produce a number of sounds (which is why dogs trained to say "I love you" sound so strange.)

While I can say that your transcriptions certainly don't fit IPA standards, accurately transcribing the sounds of non-humans is quite tricky due to how different their voice appear on spectrograms. I assume that the first consonant you mentioned is something akin to a voiceless bilabial fricative [ɸ], which is a marginal phoneme in Japanese--but is a distinct phoneme in Ewe, where it contrasts with /m/ and /f/. The other sounds you describe would be more like [ɴ̩ᵝːː] (an elongated syllabic uvular nasal with minor lip closure) for the moan and [ʔʰɸ̩↑] (an aspirated glottal release followed by a syllabic bilabial fricative with aggressive airflow) for the huff.

I studied this stuff in university, so I have some understanding of this topic