getting into Hamad hospital takes along time, if you pass all the requirements. maybe if you have connections...i don't really know. but if you come in on a tourist visa, this is good only for 28 days. you have a very short time to look for a good hospital or clinic or company so you can get your visa transferred since I've just heard that now there are no extensions for tourist visas.
....but again I may be wrong coz immigration rules in Qatar change ever so often....