Drill for Ikea dowels
Is there a specific drill [bit] I could buy somewhere?


No.

I'm pretty sure those are standard metric parts. You just use any appropriate-sized metric wood drill-bit.


  how to determine which drill size I should use?


For the wood dowels, measure the diameter and round to mearest mm. That's the size drill you need. Wood dowels tend to expand if they are not kept really dry, so round down. The most common metric sizes are 6, 8 and 10 mm.

For the metal cam-lock "dowels", you measure the inner diameter of the threaded part, like you would with any wood-screw. I think Ikea sometimes use threaded inserts for those, the thread may not be designed to cut a mating thread into chipboard. Note that some alloy-cams are very weak and brittle, I would try to find some good quality ones (or use a different type of fastener entirely)

You can do your measuring with a vernier caliper (or digital caliper if the batteries haven't died again) or just hold the thing up to the light and try various drill bit shanks behind and in front of it. A good alternative is to measure the Ikea-provided holes by dropping metric drill-bits into them backwards until you find a good fit.

You can always do some tests in scrap wood to reassure yourself you have the right sized drill-bit before making holes in any important material.

Lastly, you don't have to use Ikea hardware of course. You can be inventive with other fastening systems that work in chipboard. Screws, ordinary glued dowels, furniture-blocks, knock-down blocks etc. I sometimes have to be creative when repairing relatives' Ikea or Ikea-like furniture :-)



"Dowel points" can be useful for marking where to drill.