  This paper is devoted to investigating the Freidlin-Wentzell's large
deviation principle for a class of McKean-Vlasov quasilinear SPDEs perturbed by
small multiplicative noise. We adopt the variational framework and the modified
weak convergence criteria to prove the Laplace principle for McKean-Vlasov type
SPDEs, which is equivalent to the large deviation principle. Moreover, we do
not assume any compactness condition of embedding in the Gelfand triple to
handle both the cases of bounded and unbounded domains in applications. The
main results can be applied to various McKean-Vlasov type SPDEs such as
distribution dependent stochastic porous media type equations and stochastic
p-Laplace type equations.
