"Jeg er ikke hjemme ett øyeblikk." At least literally.
But based on my "no hits for that on Google"-gut feeling I don't think that's very natural to say if you mean to say you haven't been home at all? My dictionary says
not for a/one ˈmoment certainly not; not at all Example: I don't think for a moment that she'll accept but you can ask her. "Jeg tror ikke et øyeblikk at hun vil gå med på det, men du kan spørre henne."
I struggle to transfer "I'm not at home for a moment" to Norwegian to be honest, I can't get a grip of that use of moment... "I'm certainly not at home" is easy, "Jeg er i hvertfall ikke hjemme". "I'm not home at all" = Jeg er ikke hjemme i det hele tatt. If I use preterite "I haven't been at home for a moment" = Jeg har ikke vært hjemme ett øyeblikk.
But I had to call in sick from work today, my brains might be a bit off on this.
It's a forcing, I admit it... It was just trying to explore the possible usages. Actually, I read "øyeblikk" in the original sentence and did not realize it was already in the determinative form.
An example could be "I went to buy some milk, If you need to call me, don't use the landline, I am not at home for a moment"
"Jeg er ikke hjemme på en stund" is valid, but this time span is considerable, for a while.
"Jeg er ikke hjemme på et øyeblikk", I won't be home in an instant.
"Jeg er ikke hjemme for øyeblikket", I'm not at home at the moment.
Practically I'd settle for, referring to the essence of your example, "Jeg skal ut [en (kort) tur]/[et ærend]/[noen øyeblikk], ring meg på mobilen i stedet for fasttelefonen". I need to [go outside]/[run an errand]/[step outside for some moments], call me on my cell rather than the landline.
Insanely difficult to translate "gå ut en tur"!