LutherGooch saidI have had a Trek 1000 for several years now, but notice that others make the hills better than I. Would it be wise to start looking for a bike that could handle the hills better or is this a tale tale sign that I need more stamina?
Your bike is just fine don't worry about that. I love new equipment just as much as the next guy, but short of a better set of wheels, your best bet is just to do more hills. You can easily pick up a set of brand new ~1500 gram clinchers for pretty cheap on ebay. Lots of guys dump the stock wheels on high end bikes, and typically these are pretty good training wheels and fairly light, most likely much better than the wheels you currently have.
That being said, Hill repeats
, try to climb in staying in your saddle, only get up to get the RPMs up. Run the biggest gear you can. Keeping your RPMs above 90 on steep is tough especially when you run with big gears, but keep it over 75-80 if you can. Repeat the hills and when you think you can't do another, do another, then another. On shallow hills run them fast and don't let up, try to find long ones. If all you can find are short steep, don't fret those work too, and give you a bit of a respite on the way down.
Also try to ride with intensity. Not just on hill repeats but when out for a ride. You will get an infinitely better workout riding 20-30 miles trying to stay at or above LT than you would JRA all day.