"She is looking for a job."
Translation:Hun søker etter en jobb.
No, you can't omit the "etter" in "leter etter" if what you want to say is "looking for". If you're just "looking/searching", without an object to that verb, then you use "leter" on its own.
"Søker" does, however, work in place of "søker etter" even when it has an object.
To quote Deliciae: "Søker" does, however, work in place of "søker etter" even when it has an object.
But there are some contexts where you can't omit it. At least if the search is for someone missing, a victim or a suspected perpetrator. (A company looking for new employees can both søke and søke etter)