How can I repair a small burn hole on the front ofa Canada Goose type coat?

I recently bought a Canada Goose knock off Alpine Tec long coat and love it, royal blue in colour. I wore in on the weekend to an outdoor bonfire and not notice that an ember must have landed on the from of my coat and has burned/melted a hole in the front near the button fastners. It is in a very obvious spot and the down is coming out. Should I try to sew a wee patch with matching thread, sew a patch on the inside taken from another area of the coat......please help!