If you and your husband are fine then you can hand over the kid to your brother. And the thing you are concerned about when the girl reaches her age of maturity her Uncle would no longer be a mahram for her or would be, and that it won’t be a problem for the mother, or that if Allah has not given him why should we give him is not necessary. Just because he doesn’t have a kid doesn’t mean that Allah is displeased with him there could be a very good reason behind it. If somebody adopts a kid there is nothing wrong with that in the Islamic law. There is no such thing that it would displease Allah.
