Make a back up before you play around with this (duplicate file).
Yes, just create a symbol from the animation and then the copy and paste transfer works as long as you transfer the whole symbol.
If symbols are no option for you… you will have todo it the hard way:
- Select all involved layers or the group containig them and copy paste them to the new document.
- Select the same layers but this time all the animations (drag and hold lasso) and copy paste them to the new document.
Make sure to paste them when the playhead is at 0 (or the time you want them at)