FPT algorithm for Partial k-tree Isomorphism H.L. Bodlander in Polynomial algorithms for graph isomorphism and chromatic index on partial $k$-trees given a polynomial time algorithm for graph isomorphism when $k$ is constant.

Is there any FPT algorithm for partial $k$-tree isomorphism.
As M. Kanté pointed out, it's open whether or not graph isomorphism is FPT when parameterized by tree-width. Furthermore, I don't believe there is any complexity-theoretic barrier to creating an FPT algorithm in this case.

For a survey of what's known about the fixed-parameter tractability of graph isomorphism, see the introduction of my paper with Anuj Dawar and Eryk Kopczyński here. In the paper we show graph isomorphism is FPT in the tree-depth of a graph, which is a necessary (but not sufficient) condition for graph isomorphism to be FPT in tree-width.