It would take about 1 month or maybe longer or shorter depending on the hours you play. but once you get 80 dungeoneering and get a chaotic weapon it is very much worth it.
Also once you get your first chaotic, it has been said to be 3 times quicker for your next one :P
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I believe the Dungeoneering skill goes up to 120. The longest time it takes to get to 99 Dungeoneering depends on your combat level, as you go deeper in Daemonheim, the monster will be more powerful. Depending on you and your team mates levels the monsters/bosses levels will change also.
You need 40,000 Dungeoneering tokens, so you need to get about 400,000 Dungeoneering experience. I couldn't find any reference on how much experience you typically get per hour, and I don't have enough experience myself yet.
It depends how long you are on Runescape.
You would be looking at a good few months.
That Entirely depends on how many hours a day you play runescape.