Resident Permit (RP) is a process which starts when you land here in Qatar. It is also done by the employer. Each company has a specific person (PRO) who coordinate. As far as I know, irrespective which visa category you are on (visit or business visa) you need to exit Qatar for the employer to apply for work visa. So if your husband is brought in to Qatar by the employer, then most likely it should be on work visa and not on tourist/visit visa.

Once your husband comes here, then only the RP process starts. So like 'berake' said, all of these things like medical test, finger prints will happen only after you husband is in Qatar under work visa.
My visa was changed in beginning of July and my appointment for medical has been fixed only on 04/08. I still have to go for finger print as well. (main reason for the delay is that July is the ramadan month and things were happening slowly). But I think, now things should move fast.
And lastly, either one of you need to have the RP for your kids to be enrolled to a school. And even that, some schools have a queue.