Almost all workers who come to Qatar on work visa carry with them the printout of the visa. I did the same when I came here. As such to my knowledge, it should not be problem at all at the Doha airport. I cannot say anything about Singapore as I am not familiar with their system. However, I suggest you check with Qatar Airways in your country and they should be aware of the rules and regulations. They may be able to advise you best. Take a copy of the visa with you when you visit their office.