Is this graph transformation unique up to isomorphism? [Answer:NO]
Along with the already-given answers stating the existence of two graphs G1≠G2 for which T(G1)=T(G2), there is also a different problem: there exist pairs G1=G2 for which T(G1)≠T(G2). This is because the transformation depends not just on the isomorphism class of G, but also on the cyclic ordering of the edges around each vertex of G.

Edited to add an example based on Mark Reitblatt's comment: