Should I start working as a teacher at a different uni while I'm still finishing my PhD?
First you have to ask your advisor.  You can't just leave with 3 months left on your scholarship.  Angering your advisor is a terrible idea in a field where it's likely that everyone knows everyone else.

Second, you're going to be extremely overwhelmed at how much work it is to teach a new course.  Even though you're only teaching half time it's going to have a huge impact on slowing your thesis progress down. It's possible that you might not even finish.

However, you do have to take into account your finances.  If this is the only job you think you might get it might be necessary to pursue it so that you have income.