The ultimate goal of photoacoustic tomography is to accurately map the absorption coefficient throughout the imaged tissue. Most studies either assume that acoustic properties of biological tissues such as speed of sound (SOS) and acoustic attenuation are homogeneous or fluence is uniform throughout the entire tissue. These assumptions reduce the accuracy of estimations of derived absorption coefficients (DeACs). Our quantitative photoacoustic tomography (qPAT) method estimates DeACs using iteratively refined wavefield reconstruction inversion (IR-WRI) which incorporates the alternating direction method of multipliers to solve the cycle skipping challenge associated with full wave inversion algorithms. Our method compensates for SOS inhomogeneity, fluence decay, and acoustic attenuation. We evaluate the performance of our method on a neonatal head digital phantom.