Transferring BAT to a new computer

I have a MacBook pro that I’ve had for a long time, but I’m upgrading to a new MacBook.
I am planning on making a time machine backup of my current laptop, and migrate it all to my new laptop.

My question is, if I do this, will I still have all the BAT in my account saved?

I have like $6 on it so i’d really like to try and save it.