Well, it’s been a pukka word since it was added to the OED in 1976 .

Three Associate and Deputy Editors of the dictionary have written a detailed blog about its origin and possible etymologies (something Tolkien, as an expert linguist and inventor of languages, would have been interested in) and also correspondence with Tolkien prior to the word being included in the dictionary (the draft OED entry was sent to Tolkien for his comment).

In his replies it’s clear Tolkien was not entirely comfortable with the claim “invented by J.R.R. Tolkien”, accepting the possibility he could previously have come across the word in other texts when he was younger. According to the blog, Tolkien gave an “imaginary etymology” of the word as a compound based on two Old English words:

“the hobbits notice that the speech (of the Rohirrim) contains many words that sound like Shire words but have a more archaic form. The prime example is their word for the hobbits themselves: holbytla. This is a well-formed Old English compound (because Tolkien represents the language of the Rohirrim as Old English). It is made up of hol ‘hole’ and bytla ‘builder’”

However, the blog explains that after Tolkien died “the word (hobbit) did turn up, in a long list of ‘supernatural beings’” compiled by a Yorkshire merchant and amateur folklorist, M. A. Denham (1800 or 1801-1859), which were published in the 1840s and 50s and copies were acquired by university libraries including the Bodleian in Oxford (which would have been used extensively by Tolkien in his academic work and, most likely, background research for creating his Middle Earth fantasy world). Unfortunately Denham gave no explanation of where “hobbit” came from  

…so I guess we’ll never know

https://blog.oup.com/2013/01/oed-hobbit-definition-word-origin-etymology/