Hi Tana,
welcome on the board!
Yes, you can quilt without a frame. I quilt in a hoop on a floor stand and sometimes in a 16" lap hoop and it works just fine. I prefer thread basting because I don't like the pins, they are always in my way and the quilting thread tangles around them. Many quilters also quilt without a hoop and they are happy with it!
You can use the Search-function here on the board and you will find many threads about this topic.