No. She could decide to sleep early this evening while it's currently still morning, cause perhaps she has a lot to do today still but needs to catch up on sleep. But this would be nowhere near 'soon'. 'Soon' is always 'snart'.
Or to do it a little more abstractly: 'soon' means 'not far from now'. 'Early' means 'earlier than at the usual (or a certain) point in time'.