DO USA 3V DC 3A have a standard plug size?
DO USA 3V DC 3A have a standard plug size?

No.  None of them do.

However, you have a existing supply that it sounds like you're going to scrap.  You can get any 12 V 3 A (or more) supply you want, and attach the DC cord from the old supply to the new one.

Beware of polarity.  There is no standard for that either.  Most likely the polarity is marked somewhere on the existing supply or on the device.