This work encouraged us to do the first study of sleep, to our knowledge, in the platypus. In the platypus we saw sleep with vigorous rapid eye, bill and head twitching, identical in behaviour to that which defines REM sleep in placental mammals. Recording of the EEG in the platypus during natural sleep and waking states revealed that it had moderate and high-voltage cortical EEGs during this REM sleep state. The platypus not only has REM sleep, but it had more of it than any other animal. The lack of EEG voltage reduction during REM sleep in the platypus, and during the REM sleep-like state of the echidna, has some similarity to the sleep seen in neonatal sleep in placentals. The very high amounts of REM sleep seen in the platypus also fit with the increased REM sleep duration seen in altricial mammals. Our findings suggest that REM sleep originated earlier in mammalian evolution than had previously been thought and is consistent with the hypothesis that REM sleep, or a precursor state with aspects of REM sleep, may have had its origin in reptilian species.
pdf on the origins of dreaming REM sleep
Yeah there's a great book on this --
Animals also dream. By destroying neurons in the brain stem that inhibit movement during sleep, researchers found that sleeping cats rose up and attacked or were startled by invisible objects—ostensibly images from dreams. By studying nonprimate animals, scientists have discovered additional neurophysiological aspects of REM sleep.
Jonathon Winson pdf
The absence of REM sleep in the echidna suggests that this stage of the sleep cycle evolved some 140 million years ago, when marsupials and placentals diverged from the monotreme line. (Monotremes were the first mammals to develop from reptiles.) By all evolutionary criteria, the perpetuation of a complex brain process such as REM sleep indicates that it serves an important function for the survival of mammalian species. Understanding that function might reveal the meaning of dreams.
REM sleep could have provided this new mechanism, allowing memory processing to occur “off-line.”
The subjects of dreams are broad-ranging and complex, incorporating self-image, fears, insecurities, strengths, grandiose ideas, sexual orientation, desire, jealousy and love.
Well if that isn't consciousness I don't know what is! haha
when the hippocampus, which continues to develop after birth, becomes functional, REM sleep takes on its interpretive memory function. The waking information to be integrated at this point in development constitutes the basic cognitive substrate for memory—the concept of the real world against which later experiences must be compared and interpreted.
So yeah this really is the secret of the sense of self during "real time" Waking state -- only after the hippocampus develops for long term memory storage during REM sleeping dreaming state. Otherwise the animal just stays in the theta state while awake -- in which case the normally subconscious direct perception information would have to be processed consciously in "real time." This is the case with the Echidna that has a larger prefrontal cortex than humans relative to the brain size! But since the Echidna does not dream then it is limited in brain function to the limbic brain functions.
Without theta rhythm during REM sleep, the echidna would not be able to process information while it slept. (The echidna does, however, show theta rhythm when foraging for food.) For higher capabilities to develop, the prefrontal cortex would have to become increasingly large—beyond the capacity of the skull—unless another brain mechanism evolved.
So for the Echidna reality is like a lucid dreaming state with all the subconscious direct perception information being processed "consciously" in real time. It's a lot of information to take in at once so that the subjective experience of time is different -- this is why dreams can last in "real time" a very short time but are experienced as lasting a long time. Similarly in waking altered states as in trance meditation time seems to slow down -- or lasts longer -- because all the subconscious information is also being consciously processed in "real" time.
The Time Will Come...When All Good Things Will Be Restored... 
