No, you don't want to spend your emergency fund on the remodel. Good call
A HELOC is a possibility, but with current rates at 8.25% and climbing, you might actually be better off with contractor financing or a credit card. (I can't believe I just said that!) If you pay this off in a year (which you should be able to by saving $1000 a month), a 0% for 18 month credit card might work out better than paying $1200 in HELOC financing. Moreover, a credit card is unsecured debt, which is always better than putting your house up for collateral. One more problem with a HELOC is that you might not be able to pull a $15,000 line. They're getting more conservative in their appraisals now-a-days. (I pulled a HELOC 3 years ago on a house with AT LEAST $210,000 equity and the HELOC limit was only $158,000 based on their appraisal.)
Here's one more thing to consider (though you probably don't want to). If you wait another year you can:
1) Pay cash.
2) Make sure the renovations you think you want are really the ones you want.
3) Have a great opportunity to look for clearances on flooring/appliances/the works. You can get GREAT DEALS on re-model stuff if you're patient.