I did this trip with a mini van last year in the other direction. When you arrive in Phonsavan, just visit several local travel agencies and ask for the price. But, clearly, visit several and make your choice after. In LP, I had everything in price from $100 to $1500 (no, I'm not joking). We took the cheapest of course and had a very recent and comfy van and a very nice and careful driver. We were so happy with him and the car that we kept him for 2 extra days, to drive us around the jar plain and to drive us to Vang Vieng.
So, no need to arrange this in advance, just do it when you arrive in Phonsavan.