The approach to take depends on what you mean by "dilated". For most cases - Outset, Dynamic Offset, Linked Offset, Offset (LPE) - Tyler's answer is the right one.
If, however, you are referring to the Dilate operator in the Morphology filter primitive then things are more tricky. In that case the filtered appearance is a purely visual thing, created at the point of display. You can use Edit > Make a Bitmap Copy on the filtered object to "fix" it as a bitmap, then use Path > Trace Bitmap on that to convert to a path, but the result is likely to contain far more nodes than are really necessary.
Beyond the Basics Dilate path
Inkscape.org
Is there any way after a path is dilated to have the path follow the outside of the dilation instead of the original path?
I'd try Menu: Path>Object to Path.
The approach to take depends on what you mean by "dilated". For most cases - Outset, Dynamic Offset, Linked Offset, Offset (LPE) - Tyler's answer is the right one.
If, however, you are referring to the Dilate operator in the Morphology filter primitive then things are more tricky. In that case the filtered appearance is a purely visual thing, created at the point of display. You can use Edit > Make a Bitmap Copy on the filtered object to "fix" it as a bitmap, then use Path > Trace Bitmap on that to convert to a path, but the result is likely to contain far more nodes than are really necessary.