While well meaning, I think that's a bit much.

Look, I'm struggling with infertility myself, and it's rough sometimes hearing about everyone else's pregnancies and new babies, but I'm still happy for them. My brother apologized to me privately after they announced their latest pregnancy (now a beautiful newborn), and it was mostly for any hurt the news might have caused, and while I appreciate the sentiment, he didn't do anything to hurt me.

It's good that OP apologized, but writing a letter and giving her a gift would be making a very big deal out of it, which might even make it worse.