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Me voy a dormir - I’m off to sleep
I’m going to sleep*. You could also use it in a situation where you’re falling asleep, rather than intending to sleep. Voy en el auto y esta estación de radio está tan aburrida que me voy a dormir.
In that case, use ‘voy a caer dormido’ (I’m going to fall asleep) for more clarity.
Add - by you I mean the reader, porque por lo que entiendo tu eres español/a, ¿no?
Pienso que eres correcto. There is a word for go to bed but maybe not to sleep and I've forgotten it.