Congrats OP
NOXqs - don't accept that offer. Keep checking everyday. Bigger offers will come
Starting Score: EXP - 561, EQ - 590, TU - 573Wow! Huge increase. Since it has been only three months since your d/c, and it looks like your credit scores are rebounding nicely, I'd just continue to use your Q1 as your everday card. My nephew's d/c was in July, 2015. He started off with Q1 and the Cap One Plat., and after three months and the sixth month mark (credit steps cli), he went from $1K on both to $4K. Then, this past March, he app'd for the Venture, and was approved for $15K. His scores recovered nicely after his d/c, and when he app'd for the Venture, his Fico scores were in the 670's.
Keep checking Cap One's preapproval site periodically, and be patient Don't apply for too much credit ( keep your inquiries down), and you just may get that QS approval down the road. Good luck in your rebuild! 