I would not be concerned regarding any health risks with teak.
When I was in Thailand I saw many complete houses made from teak, and they looked fabulous. I think from memory one of them was a silk merchant John Thompson, which I would imagine you could Google it to find information.

Also be aware there are some safety issues you will need to consider with the design of cots, for instance I dont think drop sides are recommended any more along with adequate ventilation to prevent the possibility of CO 2 build up, and specific spacing and dimensions to prevent entrapment.

Have a net search in your area for any regulations and have fun making it.

Regards Rob