1. Business visa is issued for the short-terms employees or Company's visitors, consultants, business partners, etc. If your husband's company issued a business visa for you, it is (a) a violation, (b) a complication, as you will need a Family visa anyway, and you will need to switch your visa status,etc.
2. Once your husband is here, he has to obtain his residence permit (RP) first, than he can sponsor you. RP process of your hubby might take between 1 week to 1 month, depends on the Company immigration specialists. Once he got his RP, company applies for your Family visa, then you can enter Qatar on the family visa and start process of your residence permit, which also may take from 1 week to 1 month. Once your RP is ready, you can go and work right away, no need to wait 5 months. the only thing, don't forget to obtain your Work Permit once you found a Job, otherwise your work will be illegal, and may result in penalties, up to the blacklisting yourself and the company.