In this paper, we extend the coupled fractional Fourier transform of complex valued functions to that of the quaternion valued functions on $\mathbb{R}^4$ and call it the quaternion coupled fractional Fourier transform (QCFrFT). We obtain the sharp Hausdorff-Young inequality for QCFrFT and obtain the associated Rényi uncertainty principle. We also define the short time quaternion coupled fractional Fourier transform (STQCFrFT) and explore its important properties followed by the Lieb's and entropy uncertainty principles.