Most answers given so far are good. Listening to anyone will probably not cause catastrophic harm... I would be hesitant to drive 150 miles KNOWING that I have a nail in the tire, but check the tire pressure and see how low it is. If it is REAL low, like 10 PSI below the recommended pressure, then the tire is losing air and I wouldn't want to be at highway speeds when it loses all air pressure. If it isn't then you should be okay as the it is the nail that is actually sealing the hole.
I would have it repaired asap. You can use the donut for your trip; they are more durable than the warnings plastered all over it. I wouldn't go 70MPH with it, but you can use it. I would however just use the regular tire with the nail in it and pull over frequently to check air pressure and if I found a tire shop along the way that can repair it, I would do that.
Make sure they will pull the tire off the rim and use a plug/patch from the inside. This will ensure that the hole is seal, not only from air leakage, but the plug will also keep water from penetrating the several layers of tread and belts and potentially causing the tread to separate from the casing. You can also use the an "emergency" plug kit that you stick a thick string of sticky plug stuff in from the outside, but treat it like the donut. Temporary use only. First chance you get, get it properly repaired. The shop may not like that plug you used, but if they do their job right, it won't really get in the way they will cut and drill it out anyway in the process of repairing the tire.