The last published date information is not part of page model instead it is part of pagemeta model. So in page model you will see the date as 01/01/0001 which is nothing but the minimum value for date.
Use following code snippet to retrieve the last published date using DD4T:
var metaFactory = new PageMetaFactory(<Publication Id>);
var pageMeta = metaFactory.GetMeta(<Uri of the page>);
var lastPublishedDateTime = pageMeta.LastPublicationDate;
We are using this in our implementation and it is working fine. We also faced the same issue and while debugging we found that it is part of pagemeta and page.