My Duster would start stalling without warning and another thing that's weird is that it is very hard to jump start. I suspect the alternator but I hope that's not it because alternators are quite expensive. Any ideas?

Hard to jumpstart sounds like a dead battery (possibly caused by a dead alternator...) check battery voltage with engine off, and engine running. Engine running voltage (with no lights, accessories etc) on should be in the upper 13's range. If engine on voltage is same (or less) then engine off, then alternator is suspect.
A low enough battery and dead alternator could lead to stall, but it would have to be an extremely low battery for that to happen

I've run demo derby cars with big blocks and lost my alt.belt, they start to miss and stumble badly about the time the battery hits 9-10 volts, at 8 volts it becomes a wash and you have to swap the battery out. I'm the only one on my team that torture tested my batteries so I knew the 'time limit' of my car in combat....


Shoulda seen the auto parts store manager after I explained to him that those Exide 1100amp specials had a set of dead cells/bad plates after 24 hours....

-D.Idiot

I'm with D.I., its probably a dead cell in the battery. Around here, a battery is more expensive than an alternator....

If the alternator doesn't work, how long could I drive on a new battery?

You don't want to do that... you'll end up with a new battery thats dead quick. I'm assuing we are talking about a run of the mill $50 exide. A yellow top optima on the other hand.....
And from the looks of it an alternator might even be cheaper then a battery. A quick glance at kragens website shows a remaned unit anywhere from 28 to 90 bucks.

I just want to know if I'll have enough power to make it to Kragen to have them check out my alternator.