First of all, let me preface this by saying this is not an intended for an assignment, project or essay, just personal interest. Can you recommend me any valid sources regarding specific population estimates in the ottoman empire, specifically in the early 19th century? Any sources that breakdown language, religion millets, genders, social status per region are especially welcome.
The most notable and accessible demographer of the 19th century Ottoman Empire is Justin McCarthy:
I gotta be honest here, however: while, as a demographer, McCarthy's work is second-to none, I'm only suggesting him because you're specifically asking about demographic work and there's not a lot else out there in English.
The problem with McCarthy is that he has also been one of the primary voices advocating against official recognition of the massacre of the Anatolian Armenian population as genocide, including some manipulation of the data of number of Armenians resident in Anatolia in his later work (or suggesting that the genocide was justified because the Armenians were all combatants -- there being, apparently, no women, children, or elderly among them). So, it's a big asterisk, and you should be aware of it.
For me, the most accessible work--and one that I do recommend highly--on the late Ottoman Empire is Donald Quataert. The Ottoman Empire, 1700-1922. Cambridge University Press, 2005. (There was an earlier edition - Quataert was never particularly a denialist himself but had to walk a fine line due to the politics of institutions he was affiliated with earlier in his career -- those were gone by the time this edition came out and he's much more assertive here.). He does cover some of the demographics as well, and it's a very readable text.