Sure, it can be done.
Mind you, if you're asking yourself "Can this be done?" you're actually asking yourself "Can I do this?". If you're already hesitant about your skills, don't attempt this with a 110cc dirtbike engine but start doing things like this with smaller, less powerful engines.
You need some strong welds, good reinforcements etc. for this to work. A moped frame isn't made to handle the abuse a dirt-bike engine will give it.