I think they do – doves are basically white pigeons (more or less) and pigeons are known for having a magnetic sensor in their heads (not quite sure where – between brain and beak?) which allows them to navigate.
Interestingly the earth’s magnetic field is not stable and has flipped in orientation several times over the last couple of billion years. My guess is that pigeons evolved this ability after the last flip and that when the next one comes, some of them are going to be very confused.
However, even animals which don’t have any known magnetic sense have a remarkable ability to keep track of their heading. Experiments with rats revealed cells in their brain which fire whenever the animal is heading in a particular direction (e.g., North). A very recent brain imaging study from my colleagues at UCL showed that humans probably have these cells too – they used a modified video game and showed that in each person’s brain there was an area that responded more strongly when the person was heading in any one of 6 compass directions (at 60 degrees from one another), but not in the other directions.