Suppose I am analysing a dataset with two timepoints, two conditions within every timepoint and three replicates for every time-treat combination. Furthermore suppose that the hypotheses of interest are (a) DE within timepoint1 (b) DE within timepoint2 (c) differential DE between timepoint1 and timepoint2, which is basically the difference in contrasts of contrast a and contrast b. The two factors could be coded as

treat=rep(c(0,1,0,1),each=3)

time=rep(0:1,each=6)

In edgeR, after fitting a model with ~treat+time+treat:time as the design, one can make a contrast matrix to simultaneously test all three hypotheses for every gene analogous to an ANOVA, with the null hypothesis: Is any of the three contrasts false? 

How could this be done using DESeq2?

We don't have contrast matrices in DESeq2, but you can just build these three results tables just as easily:

results(dds, name="treat1_vs_0")
results(dds, contrast=list(c("treat1_vs_0","treat1.time1"))
results(dds, name="treat1.time1")