You're free to use whatever sample size you wish for your study.
However, if you intend to test hypotheses about the variables involved in your study, and your group size =4 cases, then unless the magnitude of the target effect you would like your study to be capable of detecting, should it actually exist is huge (regardless of whether that effect is some degree of group differences or some degree of correlation of scores across variables), you will have relatively low statistical power to detect when the associated null hypothesis is wrong.
If the purpose of the study is to demonstrate your proficiency at running a study using lab animals, then your proposed sample size may be just fine. But if the object is to test specific hypotheses, then the sample size might be too small.
You can get more guidance on the interplay between risk levels (for type I: "alpha level", and type II: "beta level" or its arithmetic complement, statistical power), effect size and sample size by checking one or more of these links:
The number of animals required in an experimental study depends on various factors, including the specific research question, the desired statistical power, and ethical considerations. While it is possible to conduct a study with a small number of animals in each group, using only four rats per group may have limitations.
A small sample size can increase the risk of variability and limit the statistical power to detect meaningful differences or effects. It may also affect the generalizability of the findings to a larger population. Additionally, using a small number of animals may raise ethical concerns if it compromises the well-being and scientific validity of the study.@Shaimaa M.M. Saleh