My above comment was exaggerated for dramatic effect.
I somehow missed this thread when it was opened, and after reading all of it now I wish I had missed it again.
For those with too much time on their hands:
Will Lao embassy (?) or consulate (?) in Khon Kaen issue a visa for a person who is on overstay in Thailand?
Is there any animal quarantine for taking dogs from Thailand to Lao?