Data:
DB1 <- data.frame(orderItemID  = 1:10,     
orderDate = c(\"2013-01-21\",\"2013-03-31\",\"2013-04-12\",\"2013-06-01\",\"2014-01-01\", \"2014-02-19\",\"2         
        
First, convert the columns to Date objects:
DB1[,2:3]<-lapply(DB1[,2:3],as.Date)
Then, replace the NA elements:
DB1$deliveryDate[is.na(DB1$deliveryDate)] <- 
       DB1$orderDate[is.na(DB1$deliveryDate)] +
       mean(difftime(DB1$orderDate,DB1$deliveryDate,units="days"),na.rm=TRUE)
#   orderItemID  orderDate deliveryDate
#1            1 2013-01-21   2013-01-23
#2            2 2013-03-31   2013-03-01
#3            3 2013-04-12   2013-04-14
#4            4 2013-06-01   2013-06-04
#5            5 2014-01-01   2014-01-03
#6            6 2014-02-19   2014-02-21
#7            7 2014-02-27   2014-02-28
#8            8 2014-10-02   2014-10-04
#9            9 2014-10-31   2014-11-01
#10          10 2014-11-21   2014-11-23