English Translation
We should get some sleep.
Why wouldn’t “schlafen” in this instance not be a Noun? We should get some sleep, we are getting “the sleep” not sleeping or to sleep. Does that make sense?
“schlafen” is a verb in infinitive form in this sentence, much like “to sleep” in the english equivalent “to lie down to sleep”. You can see that it’s also an infinitive in english if you insert “in order to”.
The phrase is “sich schlafen legen”. See also: schlafen - Wiktionary, the free dictionary
Of course it’s different with “We should get some sleep”. It’s a noun there.
You could translate it to german in a more literal way that keeps it a noun.
For example:
Wir sollten uns ein wenig Schlaf besorgen.
Wir sollten uns eine Mütze Schlaf holen.
Wir könnten etwas Schlaf gebrauchen.
etc.