Every distribution whose suppport is bounded has moments of every order. Here, the support is included in $[-a,a]\times[-b,b]$ hence bounded.
If the support of the distribution is included in $[a,b]\times[c,d]$ with $0\lt a\lt b$ and $0\lt c\lt d$, then the $(i,j)$-moment is between $a^ic^j$ and $b^id^j$ for every nonnegative $i$ and $j$, in particular this moment is finite and positive.