Well the data that you obtain from one animal species are most definitively useful if you want to perform experiments on different animals! For starts use on dose that you tested and observe/compare the obtained activity...that will guide you afterwards (increase/decrease dose). Also if you do same doses it will be important and significant to compare the obtained results from experiments.
Usually the therapeutic dose in rats is almost equivalent to the that dose in mice, but if you ask about the toxic dose it varies in significant aspects. If you establish an acute toxicity study to settle a new and safest therapeutic dose using mice you can certainly sure that in that dose is safe enough for rat. For selecting the perfect therapeutic dose in rats compared to mice you need to adjust a few (e.g. only +/-5%) dosage regimen only in some cases. So, dose adjustment in mice is suggested and then you can easily convert and adjust it in rats, which as well as ensures economic benefit too.
There is no simple answer and you need to examine literature specific not only for animal but for the tissue that you want to test. There is even difference between the strains of rats, let alone between rats and mice. Some differences are relative, because of inexactness of the calculations of doses of the agents (animal weight, body surface). The real differences are mainly due to the species variations in receptors or subtypes of receptors, or variations in other steps in signal transduction. I suggest you to have a look at Google or PubMed with good chosen keywords, like “pharmacological differences between rat mouse” or similar.
In our experience, there are too many differences between rats and mice, and there is no way to know before testing. So it could be that both response similarly, or very differently. Since there are differences between tissues on the same strain, much more between species. So the best way is to inject, and see. I fully agree with Dr. Pavlovic.
However, this is just one, often neglected, but not so fundamental part of the story. More fundamental is the difference that exists between tissues, even in the same organism and the same types of tissues but in different organs (smooth muscle of rat aorta and trachea respond differently). Then the differences in the same strains but of different age; and of course between different strains and spices. Those depend on different receptors distribution and other factors in the chain of signal transduction. For example rat tracheal smooth muscle (SM) is not but mouse tracheal SM is sensitive to histamine; rat tracheal smooth muscle does not react to adrenaline (I published this long ago) but mouse tracheal SM does. Before engaging in complicated recalculations one should verify whether correspondent receptors exist in both spices. Etc. The issue is complex and the simplest way is, when doing experiments, to have adequate controls from both spices..