Depending on the animal of your interest, there are several courses offered in Germany.
Usually you start with Agriculture (Agrarwissenschaft) in the Bachelor and specialize in your Masters in Animal Rearing (Tierezucht) or Animal Nutrition (Tierenährung). Uni Osnabrück offers a course in “Poultry Management” that takes between 4 to 6 semesters focusing in chicken, ducks and turkey. Another course is the „Studienschwerpunkt angewandte Geflügelwissenschaften“, abbreviated as „Stange“.
A possible ausbildung is the Tierwirt Geflügel.
With a degree in this field, you can either work as a consultant to farmers who rear poultry; work for huge slaughter houses or for companies that breed and or process poultry products.
The Nürtingen-Geislingen Uni offers a bachelor in Pferdewirtschaft while Uni Göttigen offers a Masters in Pferdewissenschaft. In BW, at the Bad Saarow Fachhochschule, they do offer a Bachelor in Pferdekommunikationswissenschaften.
Jobs in this field range from working with horse riding vereins or even working in tourist spots that offer horse riding as a sport.
One can specialize in Pig farming at the following HU Berlin, TU München or at the Uniz in Bonn, Rostock, Kiel, Kassel, Göttingen, Gießen, Hohenheim und Halle-Wittenberg. Fachhochschules that offer this include: Weihenstephan, Osnabrück or Kiel.
Currently the best jobs are working as a teacher in this field. Uni Bonn and Uni Gießen do offer the course Tierwissenschaft plus a minor in Education.
Here you can specialize in Milchwirtschaft at the Uni Hannover but no one offers a single degree based on cows.
Specializing in these fields can help one work in huge farms or even work in research to try and find better feeds for the animals.
„Marine Ökosystem- und Fischereiwissenschaften“ at the Universität Hamburg. The Humboldt-Uni in Berlin offers the english Masters in Fishery Science and Aquaculture.
Those interested in wild animals can check out Universität Freiburg’s Masters in Forst- und Umweltwissenschaften that includes a module in Wild Animal Management (Wildtiermanagement). Wild animal ecology (Wildtierökologie) is also offered as part of a Bachelor in Forest Management (Waldwirtschaft).
The Uni in Vienna offers a course in Animal therapy.
Unfortunately there is no Uni that offers a course on rabbits.