Yes I agree - space is the most important thing, and letting them out in the garden will be good when you can do it because if the newbie has room to get away you'll probably find they'll appear to be ignoring each other but actually will be sizing each other up, with fewer problems about Dolly's close personal space being invaded. You could also let them out separately during the quarantine period, for a break, and then they can look at each other through the mesh if they want to. Or of course, you could take the fairly small health risk and let them out together into the garden after just a day or two, and hope for the best. It would however, be very much better if you could give the new girl somewhere to sleep on her own until they are integrated - nothing fancy, no need for a perch or nestbox, just a waterproof box or a cat carrier with a bit of bedding in it, doesn't have to be a coop or off the ground, just somewhere she can sleep in and feel safe. She could go in a shed or garage, or indoors in an unheated place, if preferred. When you decide that you're going to let them out together the next day, go down after dark on the evening before, pick up the sleeping newbie and put her to perch in the main coop next to Dolly, who will also be asleep and won't notice. They'll then sleep together and wake up smelling the same, and emerge together, which is better than putting a new bird into a space which is defended by a resident who is awake at the time. Then let them out into the garden if possible.
In a very small run like yours it may be good to give the new bird some 'time out' on her own during the first week, to eat, drink and rest a bit. If you give her treats she will also get to know you and become tame much faster.
In the longer term, is there any way you could make the run bigger? We recommend a minimum of 2 sq.metres of floor space per hen, excluding what is taken up by feeders, drinkers, dustbath etc, which can take up a lot of space in a little run. Ideally you would create a walk-in run with the coop free-standing inside, much easier on the back when cleaning out, and good for catching a bird when needed, as well as being a large enough space for them when they are in there all day for some good reason.