Would services provided now by the government of Canada still be provided by the country of Québec ?
Yes. Québec would gradually start managing all governmental services currently provided by Canada. Those services would become even more accessible because they would be at a one stop shop!
One side effect of the current federal system is that some services fall between the cracks, as both orders of government compete to take credit for them. For example, think of how the federal government delivers employment insurance, while Québec delivers social assistance: wouldn’t it be easier for everyone if everything were at the same office? Since independence means taking full control of the decision-making process, and of the budget to bring those decisions to life, Québec’s take-over of all federal services would improve the quality of services offered.