How do you get the size of an individual index in MongoDB?

Certainly can. db.collection.stats().indexSizes is an embedded document where each index name is a key and the value is the total index size in bytes :

> db.test.stats()
{
        "ns" : "test.test",
         <snip>
        "indexSizes" : {
                "_id_" : 137904592,
                "a_1" : 106925728
        },
        "ok" : 1
}