Your giftee is counting on you and they are waiting! But if you are going to be a little late in shipping, that's OK. Please send your giftee a message from the retrieve match page and let them know that they have not been forgotten. Please don't mark anything as shipped until it has actually been shipped. As soon as it has been shipped, you can mark it as shipped at Redditgifts and submit proof of shipping at that time.
If you do ship late, Reddit Gifts will send you several reminder emails. If you are very late, your giftee will need to make a no gift report to be credited for the exchange, despite you having contacted them about the issue. This will result in you being banned from Reddit Gifts exchanges until you prove that you have shipped a gift. Proof of shipping can be submitted directly from the exchange page and any issues on your account will be resolved once your proof of shipping has been hand reviewed and accepted by a human.
This post goes over acceptable shipping proof.