DA plays fast and loose with ages, and I am unaware of any canonical reference that indicates which one is older. Robert's page says Rosamund is a year younger, but no citation is given for the source of that claim.
If you go strictly by the ages discerned for Violet and Robert, it is certainly possible that Rosamund is older than Robert. Violet was born in approximately 1842, came out in 1860 and likely married about 1862. Thus the earliest she likely would have had a child is 1863. Roberts page indicates he was born in 1866, in which case there was plenty of time for an older sibling.
The problem mainly is Robert's age. If he were born in 1866, then he is two years older than Cora, and got married at 22. We know he went to college, so is it reasonable that he got married right out of college? Also, where did he get the military experience to fight in the Boer war (1899-1902). Did he serve in the military after college and get married while in the military?
So if he was born a year or two earlier than 1866, in becomes less likely that there was time for an older sibling. While there are some here thaty would debate this point, the references giving the ages of Violet and Robert are rather weak, and allow for a bit of wiggle room.