Dreams aren't memories. Dreams and hallucinations are when your brain fires random neurons, and then it tries to interpret those random firings as sensible sensory inputs by filling in the gaps. The dream continues as the brain solidifies its interpretation and begins to self-propagate the meme.

A dog dreaming about chasing squirrel is something along the lines of random firings->that must a squirrel->I chase squirrels->squirrels run away when I chase->I continue chasing. It doesn't really require a memory of a squirrel any more than chasing a squirrel in real life requires a memory of previous squirrel. The dog just very instinctively chases small critters and knows that they usually run away.

If anything dreams are more driven by associative memory. Every input has an expected output, and you just keep chaining those together. Like spamming the suggested word on your phone's autocomplete.