Need credit card advice about age of accounts vs annual fee decision please.

Hi!

I used to have terrible credit. But then it got better. Then I was kind of an idiot and applied for Cap 1's Quicksilver. It has a $39 annual fee. Since my credit has improved, my disdain for fees and interest and has increased! In the past year I've brought my credit up well over 100 points and have only paid $7.31 in fees on another card.

Now that my credit has improved I now have this year old Quicksilver account...with a gross $39 annual fee. I've tried chatting with them online. They will not waive it.

Which is a better decision for my credit? I'd like to buy a house in about 12 months. Should I just bite the bullet and keep that card open? I have a few older lines on my account but not credit cards, just student loans and stuff. I have a few credit cards opened that are a couple of months younger than the Cap 1. No fee on those, but they're obviously even younger. Keep it open and pay the fee? Or close it and reapply under a no fee Cap 1 Quicksilver? Or heck...no CC at all? Presently I only owe that fee on my balance and they said it'd be refunded if I close the account within 30 days. So it would be super easy to close this account as I owe "nothing" on it.

Thanks for helping someone with newly decent credit!