Hi mjschliebe,
Welcome to the Sony Community!
The labels and other tags such as the ratings won't be retained when the pictures are imported to the new computer. The tags and labels are only saved in the computer or device that you're using to organize the files. Instead, I would recommend to organize and arrange the files into different folders named after the labels you used so that when it would be easier to organize them on the new device. You can import new files to the various folders in the Import window of PMH by clicking on Browse and selecting the appropriate folder.
If my post answers your question, please mark it as "Accept as Solution". Thanks_Mitch