There is a product from a brand called Eqyss which has a mosquito repellant made from marigold flowers. The marigold extract is non-toxic and is actually included in many high quality food as it is a great source of vitamins.
I work at a pet store and we sell tons of this every year (however being in alberta, canada means skeeters are only a problem for a couple of months a year), many customers love the product and say that it works very well.
The danger from skeeters is heartworm, so as long as your pup is on a heartworm preventive you should have no worries other than discomfort.
I always used a citronella oil product on my horse to repel flies and mosquitos, but don't know if it's acceptable for a small dog - or any dog - because they lick so much. I have, at times, rubbed my dogs with a leaf from a citronella plant (scented geranium) and had pretty good short-term results.
Living in Houston, mosquitos are are present nearly year-round. During the summer if they get really bad, we fog the yard if we plan to spend time around the pool at night. Citronella oil torches also help a lot to keep the worst of the swarms at bay after sunset.
The usual rules still apply: remove any sources of standing water on your property so they can't reproduce easily. Even an inch of water in a bucket is enough to get quite a hatch of larvae going. During the day, the blood-suckers like to rest in shaded areas in shrubs and particularly ground-cover plants, so if you fog, pay particular attention to those areas. Otherwise, stay inside as much as possible. With the 100-degree temps we've had for many days here, that's not a difficult rule to follow. ;-)
Avon Skin so Soft works fabulously on both my dogs. It usually has to be reapplied every day or two. There are some flea/tick/mosquito combo meds out there, but I can't remember them off the top of my head. A couple vets have told me they don't work that well for the mosquitos, because the mosquito still has to bite the dog to injest the med in order to die. Kind of defeats the purpose! If your dog licks himself a lot, you might not want to use the Skin so Soft, or check with your vet first.
I have a problem with ticks where I live. There have been cases of Lyme disease, so I have a similar worry, both for myself and my dog.
It was recommended to me to use Geranium pure essential oil, a few drops on the dog's collar, to repel insects. I do not know if it would work with mosquitoes or not. It might be a good solution if you would like to try something natural.