Select the right distribution

I have a dataset like:

dframe - structure(list(ind1 = c(1L, 2L, 1L, 1L, 3L, 1L, 1L, 2L), ind2 = c(0L, 
0L, 4L, 3L, 0L, 1L, 0L, 2L), ind3 = c(1L, 1L, 1L, 1L, 0L, 0L, 
1L, 1L), ind4 = c(1L, 0L, 0L, 0L, 0L, 2L, 0L, 0L), ind5 = c(0L, 
1L, 0L, 0L, 3L, 0L, 0L, 0L), ind6 = c(0L, 0L, 0L, 0L, 4L, 0L, 
0L, 0L), ind7 = c(1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L), d1 = c(3L, 
3L, 0L, 5L, 3L, 3L, 5L, 5L), d2 = c(3L, 2L, 0L, 5L, 5L, 3L, 5L, 
4L), d3 = c(3L, 2L, 0L, 1L, 5L, 3L, 5L, 4L), sex = c(1L, 1L, 
2L, 1L, 1L, 2L, 1L, 1L)), row.names = c(NA, -8L), class = c("data.table", 
"data.frame"), .internal.selfref = pointer: 0x0000000002661ef0)

     ind1 ind2 ind3 ind4 ind5 ind6 ind7 d1 d2 d3 sex
1:    1    0    1    1    0    0    1  3  3  3   1
2:    2    0    1    0    1    0    1  3  2  2   1
3:    1    4    1    0    0    0    1  0  0  0   2
4:    1    3    1    0    0    0    2  5  5  1   1
5:    3    0    0    0    3    4    1  3  5  5   1
6:    1    1    0    2    0    0    1  3  3  3   2
7:    1    0    1    0    0    0    1  5  5  5   1
8:    2    2    1    0    0    0    1  5  4  4   1

I would like to use the gml model to find correlations between dependent variables d1,d2 and d3 and independent variables ind1, ind2, ind3, ind4, ind5, ind6, ind7 and sex

m1 - glm(d1 ~ etiology + local1 + local2 + local3 + local4 + local5 + handedness, data = data,poisson)

Is poisson distribution the right option?