If the sapling is going to be planted in the ground then, yes, go ahead and add your dogs ashes. I'd be slightly wary if it is going into a container though.

Lovely idea! :) I add my fire wood ash to the soil all the time. No adverse effects yet.

It is a lovely idea and a great way to remember your friend. I asked the question about human ashes a few years ago but decided on scattering them with the rest of the family. Good job too because we moved last year!