I found a way to add p-value of Hausman test (and other additional GOF measures) to texreg table. This method will fetch the GOF measures automatically so you do not have to do it manually. Ask if you have any questions.
Suppose that "random1" and "fixed1" are your models
First make the Hausman test into an object
ph1 <- phtest(random1, fixed1)
Then extract the coefficients of your model
sf1 <- summary(fixed1)
names1 <- rownames(sf1$coef)
co1 <- sf1$coef[, 1]
se1 <- sf1$coef[, 2]
pval1 <- sf1$coef[, 4]
Then extract your choice of GOFs
pval.ftest1 <- (summary(fixed1)$fstatistic)$p.value
rs1 <- sf1$r.squared
adj1 <- sf1$adj.r.squared
n1 <- nobs(fixed1)
phtest1 <- fp.value.fixed1
Choose which GOFs to include in the table
gof1 <- c(pval.ftest1, rs1, adj1, n1, phtest1)
gof.names1 <- c("p\\ (F-test)","R$^2$", "Adj.\\ R$^2$", "Num.\\ Obs.", "p\\ (Hausman\\ test)")
Choose decimal places for GOFs
decimal.places <- c(TRUE, TRUE, TRUE, FALSE, TRUE)
Create a texreg object
tr1 <- createTexreg(coef.names = names1, coef = co1, se = se1, pvalues = pval1, gof.names = gof.names1, gof = gof1, gof.decimal = decimal.places)
Check that everything looks OK with screenreg
screenreg(tr1)
Repeat the same thing for all of your models (fixed2, fixed3...& random2, random3...) if necessary.
Check that everything looks OK with all models before using texreg or htmlreg functions
screenreg(list(tr1, tr2, tr3, tr4, tr5))