  The perturbative instability of NLO collinear factorisation (CF) computations
of $p_T$-integrated cross sections of heavy quarkonium production at high
hadronic or photon-hadron collision energy is discussed. We resolve this
problem via the matching of NLO CF computation with the resummation of
higher-order corrections $\propto \alpha_s^n \ln^{n-1}(\hat{s}/M^2)$ at high
partonic center of mass energies $\hat{s}\gg M^2$. The resummation is performed
in the Doubly-Logarithmic Approximation(DLA) of High-Energy Factorisation(HEF)
formalism. We also report the results of the first computation of one-loop
corrections to impact-factors involving heavy quark-antiquark pair in the
intermediate states considered in the Non-Relativistic QCD (NRQCD)
factorisation formalism for quarkonium production: $Q\bar{Q}\left[{}^1S_0^{[8]}
\right]$ and $Q\bar{Q}\left[{}^1S_0^{[1]} \right]$. These results are necessary
for the extension of our resummation formalism beyond DLA.
