Have a look at properties to rent near you or the area you want to move to and work out the deposit and the first months rent. Go on the benefits calculator to see how much you would be entitled to and take a guess at whether this would cover the bills food etc. Its really hard to estimate withput knowing your area (please dont say your area as it might be outing) but personally if ypu think you might have to leave ypur job i would want enough money for a deposit, bills, rent and food etc for 3 months to give you chance to find a job etc, but including your benefits in that amount.
Its worth considering whether you can get full time work when you move which would help with finances, and also dont forget to go thrpugh cms to claim child maintenence, he doesnt have to know where you are to pay it that way.
Just as a point, you say hes not abusive but you are secretly squirrelling away money to leave him. What would happen if you just told him you wanted to split up, because in a non abusive relationship that conversation would be possible.
Can you get a second job without him knowing and be paid directly into your account? Also its worth looking on money saving expert for things like paid surveys, they dont pay much but you could bring in a little extra cash direct to you/your sons account, to speed up the process.
I really hope you get out soon and have a wonderful life without him x