You could create a subset containing just that point and then add it to the plot:
# create the subset
g1 <- subset(a, GeneName == "G1")
# plot the data
ggplot(a, aes(log10(Index1+1), Index2)) + geom_point(alpha=1/5) + # this is the base plot
geom_point(data=g1, colour="red") + # this adds a red point
geom_text(data=g1, label="G1", vjust=1) # this adds a label for the red point
NOTE: Since everyone keeps up-voting this question, I thought I would make it easier to read.
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