Merge data.tables while keeping original order in R

I would like to merge two data tables while keeping the original order of the data tables. I would also like to have a final column to say whether the two ids match each other. All of this while keeping the original order of the data.table.

Test data.table shows the issue I am having, when you merge the two data.tables, the order of rows will sometimes be different.

If(g1.label==g2.label) then(match=="T")

library(data.table)

set.seed(100)

dt <- data.table(g1=c("A", "B", "C", "D", "E", "F", "L", "O", "P", "J"), 
                 g2=c("G", "D", "C", "H", "K", "J", "L", "U", "I", "R"),
                 value= rnorm(10))

ids <- data.table(labels=c("A", "B", "C", "D", "E", "F", "L", "O", 
                           "P", "J", "G", "H", "K", "U", "I", "R"),
                  ids=c(1:16))

test <- merge(dt, ids, by.x="g1", by.y="labels")
test2 <- merge(dt, ids, by.x="g2", by.y="labels")

# Desired output with original order
g1 g2 value g1.label g2.label match
A  G -0.50219235 1  11 F
B  D  0.13153117 2  4  F
C  C -0.07891709 3  3  T
D  H  0.88678481 4  12 F
E  K  0.86014084 5  13 F
F  J  1.09086728 6  10 F
L  L  1.42053190 7  7  T
O  U  0.93415334 8  14 F
P  I  0.22375495 9  15 F
J  R -0.35749574 10 16 F