Discrete valuation on $\mathbb{Q}(X,Y)$ such that the residue field is $\mathbb{Q}$

Question

I tried multiplicity of zeros and poles because this works for $\mathbb{Q}(X)$. I guessed that this would be the same for multivariable cases, but it looks more complicated and I don't know how to continue. By multiplicity of zeros for a two-variable polynomial, I mean the usual multiplicity defined using Hasse derivative. I know the $\mathbb{Q}((t))$ works, but I want to know whether Hasse derivative also gives a solution.