Yes, there is a new rule now that are implementing in qatar about sponsoring children from their mother but it depends on their salary.Perhaps, an employed wife can now sponsor a husband too. So, why not for the children? But 'til 3 kids only and it depends on the sponsor or employer of the wife or mother if they will give NOC too.Same processing, before the mother can apply for the visa, she can ask first NOC to her sponsor, NOC will issue by the sponsor/employer for not liabling the company for any obligations....
This what I've known from asking on my company, since I am planning to bring my children too. And upon applying for a visa, they asked me to wrote a letter for them(company)in requesting for an NOC to be submit together with all the documents and applications for the visa, coz its the immigration's requirement. Since your friend is not a husband sponsor anymore, she will do the same, i guess so...BUT to make it sure, she need to ask first her company if they can give her a family status, coz it depends also to the company she's working with.
Hope it can help.....