T.C. Albert suggests using 3-4 ounce (veggie-tanned) leather in his book on pouches. That is 3/64-1/16" thick. Leather doesn't have to be all that thick to be tough enough for your purpose. My pouch, made of that aforementioned bark-tanned deerskin, is about 8 ounces on average and is probably overkill (though I do like that thick, stiff strap, coming to think of it...)
A couple things I suggest you do before you order another pouch. First, get ahold of a couple books: Madison Grant, The Kentucky Rifle Hunting Pouch; T.C. Albert, Recreating the 18th Century Hunting Pouch; and the Book of Buckskinning, Vol. VI, which contains an article on hunting pouches. The Book of Buckskinning and Madison Grant's book are probably available via Interlibrary Loan (I know they were at one point, 'cause that is how I got them...), you will probably have to buy T.C. Albert's book. Those will give you an idea of what the historically correct choices are - for the mid 19th century you have a quite a variety to choose from.
Once you have an idea of what you are looking at, you can think about whether you want to recreate a "poorboy" set of accoutrements to go with your rifle, or a high-end set, or something in between. IIRC you aren't a reenactor. You don't have to have a persona (I don't) but it wouldn't be a bad idea to figure out what kind of person would have used the kind of rifle you are going to be using and to use that as a basis for picking out what kind of bag would go best with it.
At that point you should have an idea of what you are shooting for, which allows you to know what kind of questions to ask. Ask here, and ask the person who will be making your pouch.
In the meantime, you can be using the pouch you already have...actual use may give you a better idea of what you want functionally out of your next one.
