If the "Brake" and battery/charge lights are on, then it's the alternator. Get your Murano to a dealership immediately. Ask them to move your appointment up. Be aware that if the alternator does fail, you'll lose all vehicle power in short order.
If the warning lights are not currently on, but you think they might have been, do still bring your Murano in. It's been reported on another forum that the lights can go off for a while, then go on again. This was shortly followed by a failure.
Now, I and some others here have experienced a different problem of hesitation in acceleration, particularly after long drives. Restarting the engine corrects the problem. This doesn't sound exactly like what you've described, but I thought I'd mention it as another possibility.
Either way, bring it in to be safe and have it checked out. If it's the hesitation problem rather than the alternator, maybe they can get a code on it and troubleshoot that. Hope all turns out okay.
2003 Black/Charcoal SL AWD Prem/Leather/Sunroof/VDC/Cold Pkg