Mandi, sometimes it takes even more than 4-8 weeks, especially considering latest tightening of the rules. 6 months bank statement has been a requirement for the family visa for ages, but immigration officers could waive it in some cases, while lately they are pretty much strict over this requirement. Hence, sometimes one has to wait 4-5-6 months.
But I am wondering how you could understand the OP's post. It was so confusing, especially last "question":
"My question is, can my family not come with me in the first place with me when I am going to Qatar. In other words, can company not apply visa for my family as they are now applying for visa?
I got completely lost in this UK national's question... LOL... even using my other languages' "logic" couldn't help me and to figure out what does he want to know.. Good for you :):)