Yes. You can. Now try to sleep tonight. Apparently, the koala population is threatened by a terrible and widespread outbreak of chlamydia. And it can be spread to humans. No. Not that way.
Between 2001 and 2008, koala populations dropped 45 percent in urban areas, and 15 percent in nature. Researchers were puzzled as to what causes the sudden drop in numbers. The population has been, like all animal populations, threatened by development, but why were city koalas dying off if they were already on developed land. After some time spent on research, they got the first hint of what the problem was. It seemed that fifty percent of wild koalas were showing signs of chlamydia. There were undoubtedly more koalas who were infected but didn't show signs. Since there were no ways of treating the population and of course no safe sex, the bacteria spread from animal to animal during fighting, mating, and birth.
There are two strains, Chlamydia pecorum and Chlamydia pneumoniae. Complicating the issue, around Queensland, is the fact that the koalas there are almost all infected with a retrovirus that takes out their immune system. Fortunately, there is a vaccine available that seems to work on female koalas.
Unfortunately, C. pneumoniae can be transmitted to humans. Koala's incredible cuteness works on the disease's behalf. People enjoy picking them up, but like many tree-dwelling animals, koalas don't much care where they urinate. If an infected koala urinates on a person, they can possibly transmit the strain of chlamydia to the human. This is something you never want to explain to a doctor. Certainly not when you have to include the phrase, "I was just trying to cuddle it." So remember, when you see a koala - don't pick it up.