Good for you, MeltinMom!
I started running the same way, 30-60 seconds at a time. I was also the same weight as you. Now I run 30-60 minutes at a time and I can't imagine my life without running.
If I could be so forward as to give a bit of advice, it would be this: There is no such thing as running too little or too slowly when you're starting out. It is more about establishing a habit and not injuring or discouraging yourself.
If you just keep putting one foot in front of the other, you can achieve any running goal you make for yourself. You've already taken the hardest step in that thousand mile journey, the first one.