In DSGE model, we close model by introducing the Taylor rule. This rule perfectly caputure data in advanced economies. So my question is how to model the policy rule in developing and emerging markets? Can we apply the Taylor rule for these countries?

The reason that we model monetary policy using a Taylor rule in advanced economies is that this type of monetary policy rule describes policy quite well. You cannot generally answer this question for all emerging economies. Some are explicit inflation targeters, others use a totally different kind (or have fixed exchange rate policies). You need to take a look at the particular country in question.

Here, for example, I model the policy interest rate in Vietname (data from IMF database), and my first attempt is to model the policy rule in this country such as

i_obs: policy interest rate
i_obs_lag1: the first-order lag of policy interest rate
p_ob: inflation
y_gap: output gap
y_obs: output growth
delta_e: change in nominal exchange rate
Before closing the DSGE model, I try to estimate the equation (1) by the OLS. I do that because I would have a look at how the predicted policy interest rate differs from the actual value (see my graph) Graph.pdf (58.6 KB)

As far as I know that this country (Vietnam) follow the float-managed exchange rate regime (IMF report). Thus, would you kindly give me some comments on my strategy for modeling the policy rule for this country

Adding the exchange rate term seems advisable here. The fit looks quite good. But note that you cannot estimate Taylor rules with OLS due to endogeneity. So you cannot use the estimated parameters in your model, because they will be biased and inconsistent.

Yes, I estimate this policy rule for Vietnam by the OLS, it is because I would have some prior information for the Bayesian estimation of the DSGE model of Vietnam
So is this strategy reasonable to use the OLS estimated result for prior knowledge of the Bayesian estimation in the main DSGE model of this country?