Last year we met a cycling couple in Luang Prabang -- and became good friends! Part of this was because of their amazing round-the-world stories, and part was because of my envy..... if I had my bike handy, I would've joined 'em.
Anyway, they were headed south to Vientiane and then through Thailand. I can't answer your question specifically, but here's their website: www.gut-gelaufen.com (it's in German). If their blog doesn't fill in the details of their ride through Laos, I'm sure you could ask them in email.
We (my wife and I) didn't cycle between Vientiane and Luang Prabang. But we did go on bus -- one of the most spectacular mountain trips we've ever been on. Cycling it will definitely be tough. There are enough villages along the route that you shouldn't be stranded at night. But my guess -- as a cycle tourist -- is that it would take 5-8 days.
Good luck,
-- Mark