A tricky issue with many implications! As a single character, it should just be read doku. But it is regarded as the abbreviation of 独逸語 doitsugo or shorter 独語 dokugo which Japanese and also Koreans (under Japanese rule) have chosen to refer to the German language in the 19th century. Most Japanese natives would read it doitsugo or dokugo. As the single kanji can refer to the people, their country, and their language, in this case you have to add 語 go: language in your mind. 独逸 usually should be read doku-itsu, not doitsu as the character 独 doku usually never has the reading do. Drawing on the Dutch duits for deutsch (German) it could easily be written with phonetic katakana. In this case, however, political intention overturned and twisted the established On-reading doku, i.e., there is no consistent rule applying to similar instances.
There is even more below the surface of this issue. Why was the reading twisted and the character 独 with a beast classifier chosen and not a harmless character like 都 to or 度, 土, 戸 which are all read do in Japan? To really understand the political intention and East Asian country naming policy one often has to go beyond rote vocabulary memorization and have a look at the rarely explained ideology behind. The country naming policy of Japan and other East Asian countries is originally based on the Chinese/East Asian 華夷思想 Huáyí Sīxiăng (J. Kai Shisô):Thought that the own culture is superior and contempt of others regarded as 夷 retarded Uncivilized or ‘animals’ (and vermin) below human beings (also 中華思想 Zhōnghuá Sīxiăng (J. Chûka Shisô): Superior Land In The Middle Ideology).
If you’re in Japan, best look up these terms in encyclopedias of your local or university library. East Asians, intellectuals or other, however, usually are silent and do not openly inform about this state policy. With the Japanese and Korean choice of 独, this kind of naming today continues only with the naming of the Germans, their country, and their language. Certainly, diplomats of the German-speaking countries should work towards a decent naming. The 犭 beast classifier is traditionally used to name inimical peoples or countries one wants to put down as outsiders.
Take e.g. the name character for the Mongols up into Japan’s Edo period. As in 濛犭虎 Môko: Mongol(s), the 犭 beast classifier was added to the character 虎 ko: Tiger for further ‘beastification’ of their whole people. This ideological addendum here has no influence on the pronunciation. Compare e.g. this use in the ukiyoe series Kôso Goichidai Ryakuzu (1831) of Utagawa Kuniyoshi) as retaliation for their attacks on Japan in the thirteenth century. While in this case the beast classifier can be removed without change of pronunciation, in the choice of 猶 Yû: trick, scheme for the Jews in East Asia and Japan dropped all of a sudden after WWII it cannot. Here again it also is not just the otherwise often relatively harmless pride for the culture of one’s own realm, but the deliberate despite of others as beasts and treatment as outsiders. Understanding this is a matter of study of East Asian thought and history. Note that all these examples were established before the world wars. This is not sheer coincidence: The usage of the 犭 beast classifier started during China’s Warring States period 2500 years ago and therefore naturally breathes and sows aggression. I.e. in this case as as in others you cannot separate the pronunciation and ideology of Chinese characters! I hope that after full two years the question is now answered to your satisfaction.