Vero is about a 90 minute drive from the Orlando (MCO) airport and about 2 hours from WDW. It is fairly "self-contained" and IMHO, somewhat isolated from everything else if you do not have a car.
I agree with eva - rent a car unless you know for sure you will be happy spendng the entire time at the resort. If you plan to spend more than 3 days there, I strongly recommend a car. FWIW, I think you find that the transfer services (Mears, private towncar services) prices are comparable to renting a car.
Enjoy your trip! Vero Beach is a beautiful resort and a great add on to a WDW vacation!