You can bring your animals from your farm over to Diana's Glade, provided they aren't restricted by the usual restrictions to moving animals (i.e., you can't move baby animals, or animals currently involved in or on cooldown from a breeding).
If you have a suitable pen in Diana's Glade (for example, a pen for big animals for a Highland Cow), you can simply click on the map transfer button in their context menu to move them:
You can then click on the arrows to move (or move and turn) the animal and bring it to Diana's Glade: