We have just removed some decking from a garden we are working on at the moment. I personally hate the stuff, unless you keep it very regularly cleaned its gets slippery with algae, dogs tiddling on it will stain it and make it smell. Unless you fill the sides in very well with no gaps, it can harbour rats and mice, we found a nest under the one we removed!!! Together with Hundreds snails and spiders, yuuck!!!
If it was me I would put some wood edging (the stuff I mean is the half round connected together with wire) this will allow for water drainage, around your piece of nasty concrete and then gravel on top of the concrete. You can then use disenfectant sprayed onto the gravel to keep the dog wee smells at bay
As regards breaching the dampproof course, you do not attach the edging to the house, there has to be gap left for swelling due to water, so it cannot breech the dampproof.
Decking is going out of fashion by the way, there was none to be seen at the Chelsea Flower Show this year.