We are aware of a possible issue where players may not be able to interact with Dukino and accept missions.
An update resolving this has been released on PC (http://support.gearboxsoftware.com/entries/22126761-pc-update-information) and will be coming to PlayStation 3 and Xbox 360 in the future.
In the meantime, you may be able to complete the mission by joining a game where the host has not completed the mission "Animal Rescue: Medicine".
Keep an eye on our Knowledge Base (http://support.gearboxsoftware.com/forums) for any additional details moving forward.