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If it is Slavic, and I found ancestory boards citing it as one ancestor with the name as Slovak than it may well be related to:

Dobra (f) -- "good."

Which I found on my Russian website ...and all of the "Dob-" words bascially had the same meaning ...

http://www.sca.org/heraldry/paul/d.html

Rather than hungarian this surname is Slavic: see the site www.familysearch.org

Only guessing here ...but maybe a form of 'Tobias' ..."D's" and "T's" are often interchangeable ...

Though Hungarian is not an Indo-European language, it is surrounded by IE languages and certainly has been very influenced by them and certainly by Christianity which adopted many Hebrew names ...

Tobias, was originally a Hebrew name meaning "God is Good" ...

Your surname is rather Czech than Hungarian, but it is possible that it exists in Hungary as well.
The Czech republic and Hungary belonged to the same Empire untill 1918.
Anyhow I can't tell you anything about the meaning of the name.