Homeomorphism between $\mathbb{R}\setminus \mathbb{Q}$ and $\mathbb{R}^2\setminus \mathbb{Q}^2$

Question

Is there a homeomorphism between $\mathbb{R}\setminus \mathbb{Q}$ and $\mathbb{R}^2\setminus \mathbb{Q}^2$, where both are given their usual topologies coming from $\mathbb{R}$ and $\mathbb{R}^2$ respectively? Here $\mathbb{Q}$ denotes the rational numbers.