I'm sure one of our fabulously legal-minded VAs will post a specific reply here for you but I'm just going to pitch in that I don't see a reason for starting an LLP if all you're going to be doing with this other VA is passing along the once-in-a-while subcontract. If you don't want to share taxes/income/expenses then what possible advantage would there be to setting up an LLP?
I'd say, each of you should go LLC and sub to eachother when need be - end of story. And I'd bet that the mutual support/friendship you share will stay all the more intact for NOT being tied into a business partnership