i hope not but i give your battery a year and it'll start dying again. all you did is put a brand new battery in there that holds a really really good charge. but when the alternator goes to complete sh!t it wont charge that brand new battery anymore.I just replaced the battery when that happened to me and it worked.
...but mine wasnt when driving.
the alternator is very easy to do. based on this thread i'm assuming that you dont do many repairs and/or have a lot of tools? so your hardest part would probably be getting to the tensioner. once you get the belt off those 3 bolts and one wire on the back is nothing. when you do it just remember to remove the negative battery cable but like mentioned before you should definately make sure you dont have corrosion build up.