The English Wikipedia entry (15 Feb 2013) points out the early German and Dutch usage of the term, but doesn't give dates.   The German Wikipedia entry is more detailed, but doesn't track the history of the term itself.

The OED traces the word only to 1888:

  /ɪnˈdɒlədʒɪ/
Etymology:  < Indo- comb. form1 + -logy comb. form.
Thesaurus »
 

  The study of Indian history, literature, philosophy, etc.

1888   Trübner's Monthly List Oct. 134   There is not a single branch of Indology—with, perhaps, the single exception of Vedic studies—which will not gain very considerably by its publication.
1895   Atlantic Monthly Mar. 399.  
 but notes that this entry was published in 1900 and hasn't been fully updated.

I don't think anyone today calls themselves an "Indologian."  The OED entry for "Indologist" cites only from 1904:

Indologist, n.

View as: 
Quotations: 
Pronunciation:  /ɪnˈdɒlədʒɪst/
Etymology:  < Indolog- (in Indology n.) + -ist suffix.
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  A student of Indology.

1904   M. de Z. Wickremasinghe in Epigraphia Zeylanica I. i. p. vi,   The thanks of all Indologists are due to the Ceylon Government.
1928   Spectator 7 Apr. 535/1   Indologists at once recognized the importance of this ample..collection of material for their studies.
1929   A. Stein On Alexander's Track to Indus xii. 89   M. Sylvain Lévi, the eminent French Indologist.
1957   P. Worsley Trumpet shall Sound 224   The explanation of this absence of millenarism from Hindu India..can only be attempted by an Indologist.
1971   Illustr. Weekly India 11 Apr. 35/1   Hermann Jacobi (1850–1937) is remembered with great reverence by indologists as a pioneer in the field of Jain and Prakrit studies.

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Best,


--
Dr Dominik Wujastyk
Department of South Asia, Tibetan and Buddhist Studies,
University of Vienna,
Spitalgasse 2-4, Courtyard 2, Entrance 2.1
1090 Vienna, Austria
and
Adjunct Professor,
Division of Health and Humanities,
St. John's Research Institute, Bangalore, India.
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On 15 February 2013 14:55, Suresh Kolichala <suresh.kolichala@gmail.com> wrote:
Don't know if this had been discussed earlier, but could someone point me to the literature discussing the first use of the term 'indology'?

Thanks,
Suresh.

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