What is this beautiful lady?

We have had her for about 4 years. She was only about a foot tall and sat right in our window. She's gotten big, and we are needing to find her a larger pot.

We are wondering what it is, and maybe see if she would do well outside? We live in Phoenix Arizona and I gets pretty hot here in the summer.
If anyone knows what this is and has any tips on how we should proceed would be very greatly appreciated.
Thank you.