Is there always a free $\mathbb{Q}$-module on a set $A$?

Question

As the title says;

Is there always a free $\mathbb{Q}$-module on a set $A$?

I believe so, since you can always form the free $\mathbb{Z}$-module on a set $A$, $F(A)$ and then identify $\mathbb{Z}$ as a subset of $\mathbb{Q}$.