Is the VSEPR theory correct in determining the bond angle of sulfur dioxide?
First off, your structure violates the octet rule on sulphur and is thus not a good representation of the molecule. A better one is this one:


Figure 1: electronic structure of $\ce{SO2}$.

All methods of approximation of bond angles you have learnt or will learn about are no more than educated guesses. VSEPR gives very good approximations for e.g. $\ce{NH3}$ and $\ce{H2O}$ but fails horribly at $\ce{PH3}$ and $\ce{H2S}$. For the latter two, an estimation based on the most likely orbitals used for bonds (all p) does a much better job. To accurately determine a bond angle, one needs to perform a structure elucidation experiment such as X-ray diffraction.

This has indeed been performed with $\ce{SO2}$ (likely multiple times using different methods; I am too lazy to check the references) and the results give a bond angle $\angle(\ce{O-S-O})\approx119^\circ$. This is indeed very close to $120^\circ$ so you can say that the VSEPR method gives a good approximation of the $\ce{SO2}$ bond angle.


Figure 2: Structural data of $\ce{SO2}$. Taken from Wikimedia, where a full list of authors is available.