Oak is not an adjective in this sentence.
The word oak tree is a compound word. This means a word that combines two or more words, but it has the lexical status of being a single word.
Oak tree has its own dictionary entry in the Oxford Dictionary (OED).
Oak tree has its own dictionary entry in the free dictionary.
Third, when you look up oak in the ODO the entry says "also oak tree", meaning this is a variant or that the two are synonyms.
Some compound words are spelled with a space between the two components and some are not; some are spelled with hyphen between the two components. Compound words sometimes start with a hyphenated spelling and after a while the hyphen gets dropped. Some words start as two words and then become so common that they become a compound word (example: Chinese food).
Other compound words that are nouns include
Compound words are different from two words that are, say, an adjective and a noun. The difference can usually be heard in pronunciation.
Compare orange juice (juice squeezed from an orange) and orange juice (any juice that is orange in color). The first, like most compound words, is stressed on the first word and has a falling intonation. The second has a rising intonation on the first word. This distinction in pronunciation is true for the following two pairs, and many similar pairs:
Also key position (the position of a key) as a compound word versus key position (a position that is key or important).
A blackbird is different from a black bird, not only in spelling but in pronunication.
Most these examples are taken from the Concise Oxford Companion to the English Language and The Oxford Dictionary of English Grammar (2 ed.).
Not all collocations are considered compound words. Like most things in English, frequency of usage plays a part. Cough drop and cough medicine are compound nouns; cough trouble is not recognized as one by the OED.