Definitely don't settle for that. A healthy baby (not collicky or experiencing other health issues) should be sleeping through the night (at least 6 hours) by 10-15 weeks.
Sorry, but I'm calling bullshit. Ours weren't collicky, and they've both been perfectly healthy (apart from the occasional cold or teething pain); they just didn't start sleeping more than 3-4 hours at a time until they hit 18 months.
My point is this: if they won't sleep through the night, it's not something you're doing wrong as a parent. Read some books, try some techniques; see what works for you and your child. Don't get stressed about it.