Now, I'll start by saying that I don't see a significant problem with letting someone postpone taking a feat...a little while. Particularly when you're looking at a multiclassed character, there's often a discrepancy between when you achieve the feat pre-reqs and when you get your next access to a feat...it's especially obvious with feats that have a Caster Level pre-req.
That said - I don't believe a strict reading of the RAW would allow it. When a character advances in level, there's a specific list of things they gain and the order in which they gain them. You gain 'skill points', and you're explicitly told you have to spend those immediately, as someone else pointed out. And, as was pointed out, it doesn't say that about feats. But it doesn't need to. You're not gaining 'feat points' or 'feat slots' or 'feat choices'...you're gaining 'a feat'. Every 3 levels, "the character gains one feat of your choice". Not 'can choose later', not 'is permitted to pick'...gains. Right now.
If it makes the game more fun or more playable, houserule it. I don't think it's a problem. But if the question is 'what's the standard rule', I'm pretty convinced the intent was that you must select your new feat immediately.
(Incidentally...if you do houserule it, I suggest limiting how LONG a player's allowed to postpone taking their feat. Feats with higher pre-reqs are generally more powerful than feats with lower pre-reqs, and if you put no limit on how long people can delay, they'll hoard their picks until they can buy mega-feats. A quick, easy limit would be that you have to spend each general feat before you get another one. So, you could take your 3rd level feat at 4th or 5th, but you couldn't wait any longer than that.)