Typically if you have an organization that only talks to people with current jobs, that rule is for people sending in cold resumes. On the other hand, if they know who you are, you probably won't have the same filters applied.

Let's say you go ahead and move and take time off to watch your child. Two years down the road you want to start looking for work. What you've done with those two years is going to really matter. If you've invested time in activities like writing about your field, speaking about your field at conferences/meetups, creating an online course about your field, contributing to related open source projects, teaching a class at a university, etc. you are going to be in a very different place than someone who just checked out for 24 months.

Being currently employed sends certain signals to a prospective employer, but there are other things that can send much stronger signals. The unknown is still going to be scary and I don't know your field, but your Ph.D. can probably open a lot of doors to make yourself visible to market.