Love the idea of a vinyl plank floor but I don't like the look or feeling of walking over mouldings in the doorway.  Can this be avoided?

It is true that there are a lot of advantages to vinyl plank, and yes indeed as many of them are floating application, the expansion joints are required for doorways.  However, there are products that have rigid vinyl or composite backings that are so stable that there is no need for the transitions normally required in doorways or over larger areas.  This results in a more realistic look with no separations in the floor other than between different flooring types, and a whole main floor can be done with literally no transitions or expansion joints.  These products tend to be higher in cost, but the look is much more realistic and the product is generally a higher rated floor.  Many have attached backings to increase sound deadening and add comfort under foot while still offering a completely waterproof floor.  Use a rigid core vinyl product if the visual appeal is important to you.