Casey Anthony Video Diary -- I've ADOPTED ... a New Dog

Casey Anthony has taped a video diary entry that has surfaced on the Internet ... and in the clip, she says she's become a mother ... to a brand new dog.

The 4.5 minute video is bizarre ... with Casey sporting a short haircut and glasses ... and rambling about various topics, including how happy she is to be out of jail.

In the clip -- which Anthony says was taped on October 13, 2011 -- she says, "I'm extremely excited ... that I'll be able to Skype and obviously keep a video log ... and that I have something that I can finally call mine."

She adds, “It’s been a long time since I’ve been able to call something mine.”

Anthony was released on July 17 after she was found not guilty of murdering her daughter Caylee. However she is on probation in Florida for check fraud.

In the clip, Anthony -- who does not disclose her location -- says, "I'll be here for many many months ... even if i get off probation early."

Anthony continues, “Now I ... in some ways ... have someone to talk to even when I am by myself so I am not bothering the poor dog ... who I have adopted and I love."