R Model prediction using GLM for day-ahead forecasts in a for-loop

Basically, you have to construct a vector that contains the end dates for each run. Then, you can pick one of the end dates in each iteration of the loop, run the model and predict one day ahead. Using your code, this may look something like this:

set.seed(123)
dt.data <- data.table(date = seq(as.Date('2019-01-01'), by = '1 day', length.out = 731),
                      'DE' = rnorm(731, 30, 1), 'windDE' = rnorm(731, 10, 1),
                      'consumptionDE' = rnorm(731, 50, 1), 'nuclearDE' = rnorm(731, 8, 1), 
                      'solarDE' = rnorm(731, 1, 1), check.names = FALSE)


dt.forecastData <- dt.data
dt.forecastData <- na.omit(dt.forecastData)

Here, I construct a vector holding all days between Dec 31 2019 and Jan 15 2020, adapt as needed:

# vector of all end dates
eval.dates <- seq.Date(from = as.Date("2019-12-31"), 
                       to   = as.Date("2020-01-15"),
                       by   = 1)

Here, I create a storage file for the one-day ahead predictions

# storage file for all predictions
test.predictions  <- numeric(length = length(eval.dates))

Now, run the loop using your code and pick one of the end dates in each iteration:

for(ii in 1:length(eval.dates)){ # loop start

fromTestDate <- eval.dates[ii] # get end date for iteration
fromDateTest <- base::toString(fromTestDate)      


## Create train and test date-vectors depending on fromDateTest: ##
v.train <- which(dt.forecastData$date <= fromDateTest)
v.test <- which(dt.forecastData$date == as.Date(fromDateTest)+1)

## Create data tables for train and test data with specific date range (fromTestDate): ##
dt.train <- dt.forecastData[v.train]
v.trainDate <- dt.train$date
dt.test <- dt.forecastData[v.test]
v.testDate <- dt.test$date

## Delete column "date" of train and test data for model fitting: ##
dt.train <- dt.train[, c("date") := NULL]
dt.test <- dt.test[, c("date") := NULL]


## MODEL FITTING: ##
## Generalized Linear Model: ##
xgbModel <- stats::glm(DE ~ .-1, data = dt.train, 
                       family = quasi(link = "identity", variance = "constant"))






## Train and Test Data PREDICTION with xgbModel: ##
test.predictions[ii] <- stats::predict.glm(xgbModel, dt.test)


# verbose
print(ii)

} # loop end

As you can see, this is a bit of a shortened version of your code and I omitted the predictions for the training set for brevity. They can easily be added along the lines of the code you have above.

You did not specify which measures you want to use to evaluate your out-of-sample predictions. The object test.predictions holds all your one-step-ahead predictions and you can use this to compute RMSEs, LPS or whatever quantification of predictive power that you'd like to use.