local mums who do this pay only around $500-700, but baby goes to nanny's house. do look around before jumping into expat-targeted places.
so it sounds like they're doing babysitting, but not cleaning. That price seems fair enough for babysitting. OP wants cleaning too though.
Maybe a solution OP is to have a babysitter and a cleaner - agencies do cleaning, they can come in once per week or twice (or more if you need it, but I'm sure you wouldn't need more than once or twice per week). They can do ironing too.