Turn off Time Machine on your new MacBook Pro. Connect your old Time Machine drive, and start double-clicking:
YourTimeMachineIcon > Backups.backupdb > Old Computer Name > DateStampedFolderYouWant > YourBootDriveName > Users > LoginName > Documents
Select the multiple folders you want to put on your new machine. Right-click, and from the contextual menu, choose copy. [You need to know the total storage you plan to copy beforehand, against available. See the last paragraph.]
In the left panel of your Finder window, click once on Documents to open that folder. Right-click on the Finder window and choose paste. The selected folders from your old Time Machine backup will be copied and deposited into your current Documents folder. Disconnect your old Time Machine drive, and resume Time Machine backups on your new MacBook Pro.
The above technique would also work if you had another drive mounted as your folder destination.
Caveat: My OCZ Vertex 128GB boot drive had a caution that exceeding 50% drive space would invoke a performance reduction algorithm in the SSD controller. UNIX systems in general begin to degrade storage performance after more than 75% of the boot drive is consumed.