Going through this right now. I'm a contractor, so that means I'm constantly on the hunt. Even when employed, I always look for a better position. If accepted, offer your current employer the opportunity to match or you will go to the new company. You have more negotiating power when you have a current position in your new job as well. You can take your time and find the RIGHT position, rather than the "I need a job now" position.
"I would rather be exposed to the inconveniences attending too much liberty than to those attending too small a degree of it." Thomas Jefferson