Caveat: this is from a VAQ perspective. VFA is fairly similiar, but I can't speak for the progression in the Helo or VP worlds.
DHs typically work their way up to a "senior-level" job during their tour. They'll start at a more junior position (typically Safety), then go from there to a more senior job like Admin, Ops, or MO. OPS and MO are usually viewed as the most senior jobs, and DHs will typically get their breakout EP FITREP out of those jobs. Some squadrons may also have a Tactics Officer or other junior-level DH jobs, but it's very community dependent. I don't know if this is true for every single seat VFA squadron, but many have an LDO as Admin instead of a DH.