As above but make sure your drill diameter is slightly smaller than your dowelling also I use epoxy resin rather than glue as it forms a stronger bond.
I was always told epoxy is too hard and brittle and not suitable for bat repairs. It's ok for solid joints that don't take too much stress. I would use a good quality wood glue, it's strong and it's designed for this kind of thing. You also need to be careful when hammering in the dowel. It needs to be a tight fit but if the dowel is too big your just going to split or weaken the joint.
Well John IMO epoxy resin generally out performs glue also it isresistant to water degradation I think the key is together the mix ratio between resin and hardener correct for the job you are undertaking as it does have a toughness hope that helps.
For most epoxies the mix only affects how quickly it cures rather than the final properties, the key would be making sure you have the right epoxy for the job - as John says some of them are very brittle and no good in impact situations, you can get flexible epoxy though so maybe those would work well. Also from experience working with epoxy can be a pain in the rear end, wood glue has the definite advantage that it's very easy to deal with!