AFAIK do, re, mi, etc., are used to represent the notes of the major scale but independent of key, so for example, in the key of C:

do=C, re=D, mi=E, fa=F, etc.

And in G: do=G, re=A, mi=B, fa=C, etc. (...ti would be F#)

So there isn't a direct translation between tonic sol fa notation and keys. Unless someone else know different?