It depends on what kind of life style you want to have. I probably wouldn't pack up and go until I had a stable job for a while, even though jobs are fairly plentiful, Because you don't want to be stuck working somewhere you hate just to make your rent payment....

I'd do the same thing that any financial adviser recommends, an absolute minimum of 3 months, ideally 6 months of living expenses.. In this case I would include your anticipated rent in whatever location you're planning on moving to. 6 months of expenses living free at your parents house is a lot different than 6 months expenses in an apartment.....