Well Mott's VRH equation is correct, but VRH is not necessarily the dominant conduction mechanism in your sample. In fact, Mott's work was on amorphous semiconductors and SrTiO3 I would assume is crystalline, which means you probably have extended state conduction rather than VRH. Plus, VRH only gives you the DoS at Ef, not as a function of E.

Optical absorption spectroscopy can be a good start, since absorption of photons of energy E is correlated with the density of states at two energies separated by E. Modulated photocurrent spectroscopy can give the DoS between Ec or Ev and Ef. Photoelectron spectroscopy can give DoS as well. It really depends whether you want the DoS in the band gap, or within the bands themselves.

By analyzing the Valence band spectra obtained by UPS method you can experimentally obtain the DOS. I have done this in my previous publication

Thank you for your response. I will try what both of you have mentioned.