The ILI were really good, the fighting on the Kop was bitter, I certainly would not buy a replica QSA, if I were you, I'd just buy the real thing, in your particular case, I would actually buy an example to a recipient in the ILI, they are quite common and you should not have a problem finding one with their usual four clasps.
They had been originally raised on the 9th of November 1899 as part of the SAMIF, but, were disbanded rather early on the 15th of July 1901, so, you do often find many of their rank and file did go further to the end of the war, in another regiment.
From memory, the original 1st Johannesburg Mounted Rifles was raised on the 18th of January 1901, in Johannesburg, as a six squadron regiment, there was another corps, which was subsequently raised sometime later, the 2nd Johannesburg Mounted Rifles, but, this latter never had the same level of recruitment and ultimately merged with the original regiment, it was disbanded in Johannesburg on the 7th of July 1902.
After the war, the new administration in the Transvaal, authorised a new defence force, called the Transvaal Volunteers and a new regiment was raised with the same title, many of it's members had seen service in the original regiment during the Anglo Boer War.