Midgies start to get really troublesome from around the end of July and August is probably the worst month. They're attracted to people by scenting the carbon dioxide in the breath and only the female midgies bite because they need the blood meal to fuel egg laying. Apparently, they can detect an individual from at least a kilometre away, so in the right conditions you're likely to attract lots and lots of them, accompanied by clouds of males, and there's not much prospect of avoiding them if you're outside . They particularly like still , warm, cloudy and damp conditions. They dont like hot sun or windy conditions, so they wont be active all the time. They can be much worse than you could possibly expect, though and the only really effective tactic is to stay inside with the doors and windows closed.
Skye is a particularly midge-infested place as is most of the west coast and centre of the Highlands - mainly West of the A9.
Many people (including forestry workers) use Avon skin-so-soft which is very effective and could be suitable for a sprog - but check that with a doctor
A lot of people also use mozzie netting and you can buy head covers quite cheaply - these are gettimng to be quite a common sight.
So, one option might be to protect little Archie (and yourselves) with some fine mesh netting at the crucial times.
It will be OK when its windy, which it often is in the West.
Alternatively, go East eg to the Angus Glens or Cairngorms or Moray - all every beautiful places. There are midgies, as there are in England, but not as many because its much drier.