What time does Rosie go to bed? If she goes to bed too early, this may cause her to wake up at 4am each day, "ready" to play. A treat may help, if there is something that may occupy her for quite some time (like a Greenie), maybe try to offer that to her at 4am, but if you do it too much, she may start to expect that treat each morning.
Good luck in training her, Yorkies can sometimes mellow out a bit the older they get. Rosie sounds like she has a lot of energy!
