There is no state level prohibition due to domestic violence misdemeanors in Iowa.
The prohibited category in Iowa is crimes punishable by more than one year improsnment except for crimes classified as misdemeanors and punishable by 2 years or less. See Iowa code 724.25 for the definition of felony and 724.26 for the prohibition.
Since you have no state level disability you need onlly be concerned with whats contained in federal law.
The real question you need to be asking a lawyer is if you get the governor to give you a special restoration of firearm rights would that relieve your federal disabilty. The requisite period is 5 years from the date of conviction to apply and last I checked there was about a 50% approval rate. If you have an extensive record I think you can forget it.
Iowa is different from the feds in that to be relieved from a state level firearms disability the pardon or restoration must specifically grant you the right to possess firearms. Essentially every felon who is through with parole gets every right sans firearms. Where as federal law requires that the pardon or restoration contain a statement that it does not restore firearm rights in order to not relieve a firearms disability. This why Iowa does special restorations of firearm rights because the general restoration the governor does, does not relieve the firearm disability.
When domestic violence misdemeanors the problem becomes you don't lose any rights at the state level upon conviction so it is unclear whether or not state procedures will actually work to restore your rights. If they didn't take anythign away how can hey give it back?
Your best bet would have been to get a deferred judgment. No conviction would have rsulted and you would not have suffered a disability.