I would wait until the plant reaches mature or desired height before pruning any wood from it. Remove no more than one-third of the foliage each year.
As you know, prune soon after the blooms have faded, to avoid sacrificing next year's blooms.
Some gardeners, myself included, leave the old blooms on the plants, for winter interest. In the spring, you can usually snap off the old flower heads by hand. If you decap now, cut the flower stems just above the last leaf bud.

Should you have low branches that lay on the ground and want to create some additional plants, you can root those, by layering. Scrape a shallow trench, lay the branch in it, leaving several inches of the tip of the branch exposed, cover lightly with soil and pin it down or lay a brick or rock on it, so that undisturbed contact with the soil is maintained. Next year, remove the pin or weight and test, by gently tugging, to determine if roots have developed. Resistance to movement will so indicate.
The presence of root development can usually be determined when the exposed end of the branch orients itself into a vertical position. Once roots develop, I often leave them in place for about a year, before severing the connection to the Mother plant and relocating them.

Oakleafs and the other commonly grown native, Hydrangea arborescens 'Annabelle' are fairly drought tolerant. Around me, they have to be, to survive! But the Oakleafs, once established, seldom require supplemental watering. Many years ago, a local garden club planted several in their garden, at the entrance to a sub-division, that have performed well, even though they received no rainfall or water for 2 months, during May & June, 2007.
Be aware that Oakleafs require excellent drainage and will punish you, by dying, if planted in soil that remains wet or soggy for extended periods of time. They also bloom best if exposed to full sun or at least 6-8 hours of sunlight, anytime during the day.
Good gardening!
Rb

New gardeners (and a good many not-so-new as well) often have ill-informed notions behind the need for pruning. Pruning should not be considered a routine garden chore that every plant requires but rather approached with a clear understanding of the reasons behind pruning and what you intend to accomplish by this activity. Pruning is defined as the removal of or reduction of certain plant parts that are no longer required, are no longer effective or that are of no use to the plant. It is done to supply additional energy for the development of flowers, fruits and the limbs that remain on the plant.

Most professional pruners and the better pruning resources prioritize 4 main reasons to prune:
1)Maintain or encourage plant health by removing dead, diseased or conflicted wood (crossing branches) or thinning to lighten dense growth and provide better air circulation.
2)To train the growth of young plants (i.e., fruit trees) or to enhance the growth habit/form of more mature plants (i.e., Japanese maples, certain types of conifers).
3)To improve the quality of flowers or fruit or encourage foliar or stem effects.
4)To restrict growth or control size. And this one tends to be a point of contention among professionals as to its validity. Obviously, plants used for formal hedging need to be pruned to maintain size and a tidy appearance and from time to time various trees and shrubs will produce wayward growth that should be removed for appearance sake. But to routinely cut back trees and shrubs to maintain a size smaller than they naturally intend to be is most often a case of improper placement or the incorrect plant selection for that location and is unnecessary and disfiguring.

For a relatively recently planted dwarf oakleaf hydrangea, the only one of these reasons that could remotely come into play is the first and pruning to remove defective or diseased/dead branches can (and should) be done at any time they become apparent. Otherwise, I can hardly think of any reason to ever prune a dwarf oakleaf, other than to deadhead spent flowers, but that is really more of a housekeeping chore than a true pruning activity.

FWIW, I have a full size oakleaf ('Snow Queen') in my garden that's about 10 years old that has never been visited by pruning shears :-))

Rb and gardengal - thank you so much for your thoughtful replies. You confirmed what I suspected. I'll bookmark this thread for the future.

The shrub is so healthy, full of beautiful leaves, and has room to grow. Also, I really prefer the naturalistic look, so I won't prune. I also like the shape of the dead bloom heads.

I have it planted in what I think is a great sunny spot that drains well. So I hope it will continuue to thrive!

I really appreciate all your advice.