The word "good" is an adjective and therefore modifies nous (in this sentence, the noun "it").
The word "well" is an adverb and therefore modifies verbs, adjectives and adverbs. In the sentence "It's (going/doing) very well" the word "very" acts as an adverb because it is emphasizing how strong the word "well" is expressed.
But when describing health and well-being, we use 'well' as an adjective. If someone asks 'How are you?', in the UK we would traditionally say 'I'm very well, thanks', and the tendency to say 'I'm good, thanks' has come from the US in the last decade or two, or so I've been told. So in this case, maybe the person is responding to the question of 'How is your dog?' 'It's very well.'
Anyone know why this can't be "it is very good"? "it is" is given as one of the translations of c'est.
It was probably a bug in the program. "It is very good" is now accepted.
But Duoling said ,C'est is only used when there is a modifier or determiner ., and you are supposed to use "Il est "
"Very good" (as an exclamation) will be just "très bien" or "vraiment bien" as I heard mostly native French speakers say.
Très bon/ne is used as an adjective. For example:
I have passed a very good summer = J'ai passé un très bon été.