I pull a similar sized trailer (weight about the same but a couple feet longer) with a 1500 GMC. It does pull fine, I have no issues, but I' don't drive 70 mph down the highway....try to keep it 58-62. Do I wish I had a 2500? Sure....but like you, I pull 1 or 2 times a month for 6 months...and the rest the time the truck is a grocery getter and a commuter vehicle. Its the best balance of what I need. I've even used the 1500 to pull that trailer to Florida and to Colorado on 2 different trips...from my home in IL....2000 miles + round trip of towing each....no problem.
In the past I did have a 2500 to pull a 4000 trailer....more truck than I needed for a small trailer. I loved the truck but regreted the buy. Today, the 2500 would have been a great match to my current trailer.
All boils down to this....to me, your 04 with 3.73 gears would be perfect. You can't get 3.73 gears in a new 1500 easily.
That's my take and I'm stickin' to it!