Can I get a property visa on an off-plan property, or only a completed one?

It depends on the tier. The two-year investor visa needs a completed, handed-over unit with a title deed; off-plan (Oqood only) does not qualify until handover. The ten-year Golden Visa is more flexible: off-plan worth AED 2M+ can qualify on the Oqood interim registration, so you needn't wait for completion. Confirm current developer/DLD practice.