You could build a very simple and effective 1/4 wave loop with little cost:http://g0cwt.co.uk/magloops/new_page_2.htm
It took me less than 2 hours to build and tune my first loop and its results were very exceptional for its size.
You can use a type 43 ferrite toroid if you don't have those ferrite tubes as Ben suggests. I use both.
I also built an 80M version, 10ft vertical by 22ft horizontal. It was the most effective way for me to get on 80M from a postage stamp size yard.
You won't need a vacuum variable capacitor at QRP, but something better than a polyvaricon.
aha! Just as I suspected/feared. You've probably saved me the cost of a new tuner, and for that I at least owe you a beer. If you're ever in Milwaukee...