Why don't you propose a win-win situation to your manager, like you will leave the job in one month notice and pay the remaining month, so that you won't abandon your job just like that, and being labelled as unprofessional.

It is good to stay for one month for hand-over process to your colleagues. However, you need to negotiate with your future employer as well and describe your situation to them. Most employers will accept a one-month notice period.