Great now I'm freaking it will melt my brooder and i don't really have anything else .....
Plastic bins do not melt until the temperature is already too hot for baby birds. So it should not melt the bottom of the brooder (where the quail chicks will be.)
Because the heat lamp will be closer to the top and upper sides, they will be hotter, and it has a bigger chance of melting them. I do not know if it will, just that if anything melts, it would be the parts close to the heat.
I really think you should just set it up and see. If it does melt part of the top of the tub, change the setup a bit to avoid a repeat, and patch the hole with a piece of screen.