Does my new shower need a dedicated vent?
Local codes may be different in each area. Check with your local building inspector. If there is already a vent because you have a sink and toilet, you could possibly tie into that for drain and vent. 
I remodeled recently and moved the kitchen from one side of the house to the other. Where I ended up placing the sink and dishwasher, was on the same wall as a bathroom I had installed 3 years ago, on the opposite side. This allowed me to tie into the drain and water in the wall, which already had a vent stack. Inspector was perfectly satisfied with this setup. 
So again, I would ask your local inspector. A permit is most likely needed, and would have to have an inspection for rough and final. Best to get the vent issue taken care of before rough inspection.