These instructions are specific for Gmail, but you can most likely use the same approach (with minor modifications) with other providers and email clients too.
Press the 'Show search options'-link to the right of the search bar.
You can ignore all fields but the 'Date within.' In this field you need to enter the start date. The search will display all messages from that that and 12 months forward. Press 'Search Mail.'
Verify that the search result looks reasonable.
If the result is looking reasonable, select the messages using the button next to 'Archive' and chose 'All.'
Press 'Select all conversations that match this search.'
The last step is to add all these messages to a Label. To do so, bring down the 'Labels' drop-down and select 'Create new.'
You will now have all these messages available under a label. You can verify the result by selecting the label in the left bar.
You can now use YippieMove as usual. Enter your source account in Step 1 (the account above) and the account you want to move to in Step 2. In Step 3, you will find a list of all labels. If you only want the above messages, press 'Batch actions' and 'Deselect all folders' and then click the checkbox next to the label you created above. That's it. Let us know if you have any questions or comment.