Interesting Question....
I have seen this kind of scenario handled differently depending on where in the world you are.
I have worked rules whereby if the arrival flight is within 5nm of touchdown, you cannot launch a departure unless you can apply reduced separation. On the other hand, I have worked at airfields where the scenario is completely disregarded.
The main issue in my opinion is that you have to plan for the event that the arriving flight goes around. In this situation, I have heard some people say that emergency separation may be applied as it is an unplanned event however,
My opinion is that assuming both flights are IFR and you are inside CAS, you should never put yourself in a situation whereby you cannot provide standrd separation in the event of the arrival going around. This can mainly be achieved by applying a form of departure separation to flight which is going around.
For example, if your departure routes on a SID which is separated from your Missed Approach procedure by 45degrees or more, you could argue a 1 minute split is acceptable and therefore, you can launch a departure when the arrival is more than 60 seconds from touchdown.
Alternatively you may elect to use a form of vertical if the departure is likely to have cleared your MAP altitude by the time the arrival reaches MAP.
Either way, (in my opinion) if you can't provide standard IFR separation or reduced separation between the two flights, you probably shouldn't be launching the departure.