  In this paper we propose algebraic universal procedure for deriving "fusion
rules" and Baxter equation for any integrable model with $U_q(\widehat{sl}_2)$
symmetry of Quantum Inverse Scattering Method. Universal Baxter Q- operator is
got from the certain infinite dimensional representation called q-oscillator
one of the Universal R- matrix for $U_q(\widehat{sl}_2)$ affine algebra (first
proposed by V. Bazhanov, S.Lukyanov and A.Zamolodchikov for quantum KdV case).
We also examine the algebraic properties of Q-operator.
