I am decided to buy a monopod. I wonder if I will be allowed to take it on a plane in a carry-on luggage? If there is a high chance for it, I would rather buy the one that folds into smaller item, preferably one made of carbon fibers.
You usually can and they will usually let you.
Obviously it has to fold within the carry-on specifications of the airlines and the security regulations of your departure and transiting airports.
Note that it is best to carry a printed version of the applicable regulations with you to avoid the case where you can but the do NOT let you.
With certain combinations of departure airport, airlines and destination you may be subjected to a different set of regulation at some point before the gate. In such case you should check both regulations printed. The only thing is that I have not found a reliable source which indicates the while regulations apply to which combination.
There are reports on forums of dpreview, Fred Miranda, photokb and boards.ie from users claiming to have done it, most of them several times. On the other hand, Overclockers Australia has several people telling negative experiences.
As long as you meet dimension and weight limitations and don't have spiked foot on the monopod, I see little reason why it should be considered a hazard. But similarly shaped pool cues are in listed as forbidden to carry-on by TSA. No mention of tripods/monopods in that list, but there is a note that the list is not intended to be all-inclusive. And a security officer might classify it as a tool longer than 7 inches, which is forbidden to carry-on.
So, as a conclusion - you might end up with a security official who has had a bad day, but I'd consider this a slim chance. If you have check-in luggage, just put your monopod there to be sure; travelling light, you'll probably be okay carrying on too.
I routinely pack my tripod in my carry on here in the US. I have once had a screener say it wasn't allowed. My answer was, "ok, I'll just go back out and put it in my car and then come through security again without it." He grunted "ok" and had someone else show me the way out of the secure area. (she apologized for it as we were going and stamped my boarding pass with a priority pass to skip the line.) I went to the next security checkpoint down the concourse and breezed right through.
Not carbon, but definitely compact, the Twig Pod folds like a tent pole, and pokes into the ground to stand on its own. This is a short pole, best suited for a compact camera, but for $28, it looks like it might be worth a shot.