Unfortunately it seems it will be quite expensive according to this thread titled "Moving household goods to Vietnam from BKK". In summary:
On April 10th, 2019 a person received a quote on 18-20 cubic meters of household goods from BKK to Da Nang for $7200 USD.
That quote didn’t even cover storage:
I just received a quote for 215K baht plus a 7% VAT for shipping 18-20 cubic meters of household goods from BKK to Da Nang. That is about $7200 USD just for shipping. Add in the Vietnamese duties for electronics(40%) and furniture (10%) and the potential cost for customs inspections and I would have to seriously think about moving anything. Too much paperwork and too many unknowns. If I was certain of the process and charges at the Vietnamese end it might be worth it but I need to do some more research. 28K baht solved the customs issue in Thailand so maybe a similar situation is available in Vietnam.
It seems to me that it is best for most people in Thailand to sell their stuff before moving throughout Asia.
Credit:stackoverflow.com‘