I am analyzing RNAseq datasets with a bit complex experimental setup. Specifically, I have 6 strains, each of which has 2 time point for control and drug treatment. ie, 642 biological replicates=48 samples. As I know, one way of analyzing the data is to make a time point based pairwise comparison by makeContrasts and I used (edgeR),

group<-factor(paste(targets$Treat,targets$Time,targets$Genotype,sep="."))
cbind(targets,Group=group)
y<-DGEList(counts = raw_counts, group = group)

#Filterout low count genes
y<-calcNormFactors(y)

design<-model.matrix(~0+group)
colnames(design)<-levels(group)

y<-estimateDisp(y,design)
fit<-glmQLFit(y,design)

my.contrasts <- makeContrasts(DrugvsControl.2h.rk1=Drug.2h.rk1-Control.2h.rk1,  levels=design)

qlf<-glmQLFTest(fit,contrast = my.contrasts[,"DrugvsControl.2h.rk1"])

I would like to know if estimating the pairwise DEGs at each time points and intercepting with DEGs from other time point(as am planning to do) is a valid method to analyse the given experiment? Is there any dimension that I can apply to improve the analysis? Basically my aim includes identifying genes up or down regulated at each point across all genotypes, genes that show response at a specific time point across all genotypes and some contrasting response patterns.