Telling someone to buy a bigger truck is easy when it's not your money....
To the OP, if the Avy is in good mechanical condition then it shouldn't have much issue with a 7000lb trailer if everything is properly set up, trailer brakes, wd hitch in your case and I'd reccomend an additional transmission cooler if it doesn't have an external cooler and a trans temp gauge.
All that said, there are a lot of variables that none of us know about with a 15 year old truck and your particular trailer.
That's a lot of trailer if the Avy is ragged out, high miles, needs work.
But by your admission, you thought it towed well and acknowledge that you need to get it setup right and the brakes? Fixed on the Avy, so with all that it sounds doable to me.
This coming from a guy who just hooked 14klbs to my Silverado 1500 a couple days ago. It was just a short jaunt though.