Making some calculus I end it up with the following expression:
$$\int_{\mathbb{R^2}} dxdy\ \delta(x - y)\delta(x - y) = \int_{\mathbb{R}} dx\ \delta(0) \tag1$$
Taking into account that
$$\int_{\mathbb{R}}dx = \int_{\mathbb{R}}dx\ e^{ixt}\Big|_{t = 0} = \delta(0)(2\pi) \tag2$$
Then, would Eq. (1) be equal to $[\delta(0)]^2(2\pi)$ or there is another way to compute this? Maybe there is some property of Dirac delta that I don't know, that's why I'm asking