No, you should not drive a Jeep Liberty (or any vehicle) with only one quart of oil. This is extremely dangerous and will likely cause catastrophic engine damage. A low oil level means insufficient lubrication for the engine's moving parts, leading to overheating, seizing, and ultimately, a costly repair or replacement. Even a short distance could be enough to cause irreparable harm.
Check your owner's manual for the correct oil capacity for your specific Jeep Liberty model. Add the necessary oil immediately, and if you're unsure how to do it safely, take your vehicle to a mechanic.
