since you were married in the philippines you may need to register your marriage there. it needs to be registered in the office of civil registrar (i think it needs to be registered in the municipality where your wedding took place, not sure though) and the nso. ask your wife to do it since she's there. i don't think the philippine government cares whether she converted to islam or not, unless she needs to divorce her former husband or something else allowed for muslims which christians are not entitled to.

after it's registered in the nso, tell her to bring a copy of the nso-attested marriage certificate to the dfa and get a red ribbon there. after that get it attested with the qatar embassy in manila.

as far as i know, there is no such thing as an agency for marriage affairs. deal only with government employees but take care of getting scammed by people roaming within those government offices. they're called fixers and they're everywhere. do not be stupid enough to fall for them or you'll end up getting fake documents.

if you don't have enough money, ask your wife to approach the public attorney's office of their city hall, or a university's office of legal aid (if a university has a law school, most of them would have one). they give free legal advice. some of them may have shariah lawyers. i would suggest the university of the philippines' college of law. the university also has a department of islamic studies and might be able to help you. but that would depend on where your wife is in the philippines at the moment. if she's in mindanao, there are a lot of good universities (like siliman university, i think) that teach islamic law as well.