Welcome to the forum
I suggest an online search for agents. Have you asked any work colleagues for help.
There are often house rentals advertised in the windows of expat type grocery shops around Vientiane.
Rental houses are expensive in Vientiane. You may be better off looking for an apartment.
Until you find something, and to give you time to do so without rushing, perhaps a guesthouse or smaller hotel will suffice for a month or so. The rates can be negotiated for long term stays at hotels, guesthouses.
I bedroom apartments can be found for $300 to $500. 2 Bedroom from $600 upwards. Houses go for $1200 up to $3000 or more.