The author considers the following doubly nonlinear SPDE driven by a Brownian motion \((W(t))_{t\in[0,T]}\): \[ \begin{array}{l} dB(u)-\text{div}_xA(\nabla u)dt = \sigma(u)dW(t)\qquad\text{in }\Omega\times (0,T)\times D,\\ u = 0\qquad \text{on } \Omega\times(0,T)\times\partial D,\\ u(0,\cdot) = u_0(\cdot)\qquad\text{in } \Omega\times D,\end{array}\tag{1} \] where \(D\) is supposed to be a domain in \(\mathbb{R}^d\), the operator \(B\) is given by \(B(u)(x):=b(u(x))\) for some differentiable function \(b\,:\,\mathbb{R}\to\mathbb{R}\) with \(b(0)=0\), and the nonlinear drift operator \(A\) is the Nemyckii type operator \(A(L)(x):=a(x,L(x))\) for some Caratheodory function \(a:D\times\mathbb{R}^d\to\mathbb{R}^d\) and a measurable function \(L\,:\, D\to\mathbb{R}^d\). The author defines the notions of weak and strong solutions of the considered SPDE. Under some additional assumptions on coefficients of the equation, the author shows the well-posedness result (in the sense of weak solutions) for the corresponding deterministic ”skeleton equation”. Then, using monotonicity arguments and weak convergence approach, the author proves large deviation principle for the strong solution of (1). Furthermore, the author proves existence of an invariant measure for the semigroup associated to the strong solution of (1) using some a priori estimates, sequentially weakly Feller property of the considered semigroup and the Maslowski-Seidler modification of the Krylov-Bogoliubov technique.