Submodules of $\mathbb{Q}\oplus \mathbb{Q}$

Question

I'm trying to find a description of all the submodules of $\mathbb{Q}\oplus \mathbb{Q}$ as a $\mathbb{Q}$-module, particularly the simple and maximal ones. So far I am happy that $\mathbb{Q}\oplus 0$ and $0\oplus \mathbb{Q}$ are clear simple, maximal submodules. Now I think $(a,b)\mathbb{Q}$ where $a \neq b$ and $a,b \neq 0$ are also submodules. I think these are also maximal and simple but I'm not too sure how to show this.