First time cooking a vertical chicken

350* indirect will be do the trick.  Beer can adds nothing so skip it for this cook.  If it will balance, put the chicken upside down on the holder.  That is have legs up in the air and breast down.  The egg will be hotter higher up in the dome and you want the thighs to cook to a higher temp than the breast.  

I haven't done a bird that small in a while, so I'd guess 45 minutes to an hour.  At the 45 minute mark, check the breast for temp with a target of 160* - 165*, knowing it will not be the same temp everywhere.  My criteria is check multiple spots and pull when all tested spots are 160* or higher.  That means some spots will be as high as 165* - 170.  

Some people will accept one spot as low as 155*, but I'd be cautious about going that low unless you have a very accurate thermometer and know the spot has been at 155* for at least a minute and preferably 2 minutes.  I've done high 150's on bigger birds where its tested mid 150s and then high 150s on a test a few minutes later.