Let $G$ be a topological group which is totally disconnected. Then one point sets in $G$ are closed, and hence $G$ is Hausdorff.
On the other hand, we have a notion of a locally profinite group, a Hausdorff topological group which has a neighborhood basis of the identity consisting of open compact subgroups. A locally profinite group is obviously totally disconnected.
Is there an example of a totally disconnected topological group which is not locally profinite?