It sucks but I think you're in the right mindset to turn this into a positive more than anything. You weren't happy there and it wasn't good for you and now you don't have to even juggle working and looking for a new job.

Plus being fired without cause is basically the best case scenario for leaving a job you weren't happy with, and doesn't negatively impact job searching. I don't know about there but here you're practically guranteed to be covered by unemployment if you can show you were fired without cause and are looking for a new job.

Take some time for yourself to relax and spend some time with your dogs then you can move onto your next thing.