Ask to gate check it and they get put in last then and they often give it to you as you walk out of the plane. I've travelled loads with buggies (including an urban tourer when dd1 small) and never had problems.
who are you flying with MrsP? I've had some horrible experiences with damaged pushchairs and so now only ever take a cheap buggy. Only okay for a holiday where you don't plan on doing much walking though. I'm not sure a bag will really help with protecting your pushchair though. A strap around the outside to keep it tightly together might be a good idea though.