Let $k$ be a field and let $C,D$ be two integral curves in $P^2_k$. Now let $f:C \to D$ be a birational isomorphism. Can $f$ be extended to $P^2_k$. To be precise, does there exist a birational isomorphism $F:P^2_k \to P^2_k$ such that $F$ and $f$ agree on a (non empty) open subset of $C$?

I am mainly interested in the case when $k=\mathbb Q$.