I looked into it from the Nong Khai crossing to Vientiane and you need to go to the Thai offices and get documents, plus provide a few too yourself, and stipulate when crossing and for how how long etc etc etc, at least a days notice too. You can do it but I thought it was better to just leave the motor in LOS and just go over on foot, rent a car on the other side.
A foreigner driving in Laos with Thai plates is a magnet for problems imo, plus if it got nicked then you can expect zero help for the Laos authorities, even worse than here in LOS and you would then have to go through the hoops with the Thais on the way back if you're not bringing a car back with you, they might think you have sold it to a crim, happens all the time, hence the drama to go through the crossing in it in the first place, plus you would need special insurance too as the normal Thai insurance sure as hell wouldn't cover you for a jollies trip to Laos.
Don't bother imo, a drama waiting to happen and once you get away from Savannakhet and drive into Laos then you are into the southern districts with silly/petty commie local officials that hardly know the law and only understand/care for the law of the pocket. There is even less law in evidence in Laos that there is in Thailand, you're on moving groung in LOS but it's way worse in the 'Please don't rush' republic, and they always only just see you as a easy target. You are OK in the touristy areas, but if you venture to the 'paths less trodden' there then it's probably better just to rent a car in Laos.
When I have gone to the border I have just left my wheels on the Thai side and gone across, no dramas. In Nong Khai, there is somewhere to leave a car/pickup whilst you venture over, there will be one in Mukdahan too someplace even though I'm not sure where it is as haven't been to Mukdahan for about 3 years.
However, up to you man.
