Function to run kappa2() and agree() (from the package irr) cycling through several columns using the split-apply-combine paradigm

I'm new to R and I'm working on a test-retest analysis using Cohen's kappa on several questions from a survey that was administered at 2 different times.

I wrote a function to run kappa and agree (from the irr package) cycling through several columns using a while statement that takes the first two columns from a dataframe as arguments for kappa2() and agree(), and then the next two columns, and so on. Here is a sample of the dataframe and the function:

Q1T1    Q1T2    Q2T1    Q2T2...
1       0       0       1   
0       0       0       0   
1       1       1       1   
1       0       0       1   
1       0       0       1   
1       0       1       0   
1       0       1       1   
0       1       1       0   
1       1       0       1   
0       1       1       1   

a <- 1  #argument for the first column containing question 1 at time 1
b <- 2  #argument for the second column containing question 1 at time 2
c <- 3  #number of questions
while (a < c * 2 + 1) {
  kap <- kappa2(select(dat,a:b))               #Use this line for unweighted kappa
  #kap <- kappa2(select(dat,a:b), "equal")      #Use this line for weighted linear kappa
  #kap <- kappa2(select(dat,a:b), "squared")    #Use this line for weighted squared kappa
  agr <- agree(select(dat,a:b), tolerance = 0)
    ttl <- paste("Question", a %/% 2 + 1, "-")
    cat(paste("..............................................................",ttl, sep = "\n"))
    print(kap)
    print(agr)
  a = a + 2
  b = b + 2
}

Is there a way to do this kind of cycling using apply(), lapply(), sapply(), or tapply() instead of the while loop? I feel that my function, although it works, is not a very R approach.

Thanks!