Hi!
Sorry for taking a backdoor to this ongoing post sequence :).
I think, it is better idea to come to Qatar on your husbands sponsorship. In other words your husband could look for a family RP which of course will include your children. The advantage of doing that will be...

1 You will get to stay with your husband as a normal family.
2 You will be in a better position to negotiate. For employer it is almost always a plus to find someone available locally.
3 You can continue to remain in your husband's sponsorship still be employed somewhere. Some employers prefer that, they don't have to take the burden of providing accommodation, yearly ticket etc. What they save might reflect in you pay packet.

And yes...you can continue to stay and work here as long as your husband is employed.

good luck