Is a Female dog and a male monkey able to work it out?

Definitely yes. They will have a great life and they attractive to each other. Monkey's charm will win Dog over easily. In return, Dog pledges lifelong loyalty.
However, dog female is an idealist while the monkey man is an opportunist. This can cause a difference that may become too large to overcome.
Generally speaking, it is a good pair and if you love each other deeply, that will be wonderful.