Let p be an odd prime number and g < 2 be an integer. We present an algorithm for computing explicit rational representations of isogenies between Jacobians of hyperelliptic curves of genus g over an extension K of the field of p-adic numbers 𝒬 p. The algorithm has a quasi-linear complexity in the degree of the rational representation. It relies on an efficient resolution, with a logarithmic loss of p-adic precision, of a first order system of differential equations.