The play vanity is extremely sturdy even with the weight of the mirror. The corbels provide additional support and I added 1×2 vertical brackets on the back side (see down below) to keep the mirror in place.
I choose a simple 3/4″ moulding for the top surface edge which mimics the routing on the corbels:
2. For the mirror make a frame to fit over your mirror:
And attach to side of mirror using pocket holes: