I am currently working as a software engineer and have a pretty good salary (above $125K). How much savings should I ideally have before quitting my job and working full time on a startup idea solo (just myself, without a cofounder or employees in the beginning)?
1 year sounds about right:
It is not about how much as a number. you need first to make sure that you launch at the same time you are quitting and that you are not missing any major part in your start up. you should know that you wont be having an income from your business for sometime so make sure you have what covers your personal expenses for sometime until you start gaining from your business. Always keep a safety limit in time and money and put all the options on the table in front of you so you could have more than one plan.
Ideally its a minimum of 6 months worth of expenses plus estimated capital for your start up