That is a "Bad Idea"™
If something happens to your incoming transaction (the sender double spends it) or it never confirms because of low fees, then your outgoing transaction will never confirm... It certainly won't increase the speed at which the person you're trying to send coins to will receive them as confirmed.
Just because your inbound transaction suddenly gets a confirmation, doesn't automatically guarantee that your outbound transaction will suddenly get a confirmation. It is dependent on network load and fees etc.
I see, thank you, so what is the best course of action then? Wait for 6 confirmations?
What HCP said is correct. However, just to add on something. If you include a high fee on the subsequent transaction that uses the output, it can potentially get your previous transaction confirmed faster. Some miners have CPFP enabled and if they see that your "child" transaction has a high fee, they would be incentivised to mine the whole chain of transaction for you.
Just 1 confirmation, I've never really seen anyone double spending after a confirmation. The risk is there but its too small for most to care anyway.