Dog vs dawg pronunciation

TLDR: I believe this depends on when the text you're reading was written. It likely indicates an alternate pronunciation, but which alternate pronunciation depends on context. If the text is fairly recent, it may indicate an African-American Vernacular English (AAVE) pronunciation of dog with a diphthong. If the text is American and was written between 1840 and 1940, it quite likely indicates a non-standard pronunciation that educated people generally didn't use then (although today it's one of the most accepted pronunciations). It might also indicate the usual pronunciation of dog. I don't know what dawg would indicate in British texts.

In the late 19th and early 20th century, the accepted pronunciation of dog among educated Americans was /dɑg/, with the vowel of dock, and /dɔɡ/, with the vowel of dawn, was a non-standard pronunciation. You can see this because dictionaries from this period gave the pronunciation [dɑɡ].

Authors would use the spelling dawg to indicate that a speaker was uneducated or rural. This puzzled me as a child, because I pronounced the word [dɔɡ] and I couldn't figure out what pronunciation the spelling dawg represented.

Today, half of Americans have the COT-CAUGHT merger, and can't tell the difference between the pronunciations /dɑg/ and /dɔɡ/, and most of the rest of us use the formerly non-standard pronunciation /dɔɡ/, so to indicate this pronunciation you don't need an alternate spelling today ... it should be spelled dog.

From Google Ngrams, I suspect the pronunciation /dɔɡ/ was non-standard roughly between the years 1840 and 1940, because this is where the spelling dawg is most common. There's also a more recent peak, since around 2000, which must indicate the AAVE pronunciation of dawg, which is something like [dɒʊɡ].

There's actually even another possibility. New Yorkers use a diphthong for some words thata contain the phoneme /ɔ/, like coffee and dog — something like [kɔəfi] and [dɔəg] — and you sometimes see the spellings cawffee and dawg used to indicate this New York pronunciation.