Since you can’t observe another creature’s dreams directly, there’s really no way to know for sure if it’s dreaming. But there’s some pretty convincing – though indirect – evidence that many other mammals do indeed dream.
This evidence stems from the fact that for humans, a stage of sleep known as Rapid Eye Movement sleep – or REM sleep seems to correspond with being in a dream state.
During REM sleep, your eyes dart back and forth, you can’t move much, and there’s lots of electrical activity going on in your brain. Almost all mammals that have been studied – from dogs and cats to duck-billed platypuses – seem to go into this stage of Rapid Eye Movement sleep. The patterns of electrical activity in the animals’ brains during this stage are similar to those of humans.
So, if these patterns show that humans are dreaming, then it seems to be that these animals are dreaming, too.
Studies have shown that cats who were altered to move during REM sleep ran around, swatted their paws and bit at imaginary objects. So, not only do we have evidence that cats dream, but we have some idea of what they might dream about! - Millet

It is clear to me that my dog dreams-- at times while she is sleeping you can see her legs going through limited motions of running and she makes muffled sounds like barking or whining.