Recently, short packet communications gained significant attention due to the advancements in finite blocklength information theory. However, performance of short packet communications over interference-limited scenarios under channel uncertainty have remained largely unexplored. This work investigates the performance of treating interference as noise and joint decoding schemes in two-user Gaussian Z-interference channel under finite blocklength coding regime. The average error and throughput of the two-user Z-interference channel are characterized for different schemes in a Rayleigh fading scenario. However, the average throughput does not take account of the bursty nature of the data arrivals at the users. Thus, we consider the stability region as a metric, and it is characterized using the probability of successful decoding at the receivers. The average error developed for the different interference mitigation techniques under the finite blocklength coding help to obtain the stability region. A main takeaway message is that even for the weak interference regime, the joint decoding scheme can perform better than the treating interference as noise scheme for low rates.