I did this last night..

You can select a group of keys in the Dope sheet then slide them to the right with no problem. I've never inserted a key in the Dope sheet but I think you can. If not, just insert it in the graph editor then go to the dope sheet and slide things over to the right.

I also discovered that you can scale your animation up or down in the dope sheet so that it can take longer or shorter to play..