Should I switch from Ativan to Klonopin to taper?

I am currently on .5mgs 2x during the day and 2mgs at bedtime. I am having terrible breakthrough anxiety. I wake up in an anxiety attack each morning at 5 am. My doctor offered me to switch to Klonopin 1-2mgs at bedtime. I feel like I need to stabilize before I can begin to taper and I dont feel stable on the Ativan at all. Should I switch to Klonopin first, stabilize, and then taper from there? Anyone out there who has done this? Thank you!