You are ranking on the 3rd page of Google results for the term "doktor" which means "doctor".
There are so many issues it's hard to pick a starting point.
1. The term "doktor" is very generic. Frankly, your current rank at the top of page 3 for such a generic term is higher then expected. You are competing with every doktor related site in Turkey. Some examples: Dr. Who ( a popular tv series), medical doctor, non-medical doktors, descriptions of the degree, etc. There are over 100 million results for the term. How did you conclude there is no competition for the term?
2. Your title is not optimized for such a term as doktor. Your page title is "En Hızlı Doktor Sitesi | CevapSepeti.com" which translates to "The Fastest Doctor Sites | CevapSepeti.com". You rank on the first page of Google for "En Hızlı Doktor Sitesi" which is the keyword your title is optimized for.
3. Your header is not optimized for the term "doktor". The current tag is "DOKTOR BULMAK ARTIK ÇOK KOLAY"
If you wish to see a web page optimized for the term "Doctor", here is one: http://en.wikipedia.org/wiki/Doctor
Based on your question and the information you shared, the problem is not Google but your understanding of how search engines work. The goal of a search engine is to provide the search results desired by users. Based on Google's results, most of the people on the planet agree Google does a better job then anyone else. If people disagreed, they are free to use another search engine.
Have you checked Bing? Bing.com.tr does not even show your site on page 3.