A criminal conviction stays on your record forever unless you get it expunged. You were probably charged with a misdemeanor. There really isn't a crime called "Domestic Violence" in any state as far as I am aware. Certain crimes are given a domestic violence tag if they involve family members or people who live together, but the underlying offense is what will determine whether you were convicted of a misdemeanor or a felony.
Most domestic violence cases involve misdemeanor charges like simple assault. Find out what the actual conviction was. Was it assault? If so what, what degree? Was it malicious mischief? If it was something more serious like attempted murder or rape, then your domestic violence conviction was a felony. You need to find out exactly what you were convicted of. Felonies carry sentences in excess of 1 year while the maximum sentence for a misdemeanor is 1 year. If you were told that the maximum sentence for the crime you were convicted of was 1 year or less, than it was a misdemaenor.