I think I've seen these stickers that you can stick onto baby's clothing that is supposed to keep mosquitos away. However, my baby is a newbie so I haven't had a need or the chance to go looking for them. I saw them once at a garden wedding and the mom told me they were made by a Japanese company...therefore maybe Eugene's would have them? Might call ahead and ask though since I'm just guessing here.
Also, once you're bitten (not for the baby, but for you), immediately wash with soap and water to get rid of any lingering poison. And if you're super allergic like me, you might take an antihistamine, which will prevent the poison from reacting and basically kill the bite before it has time to create a reaction (as you know, once the reaction sets it'll take days to heal and be itchy the whole time). I have no idea if this is particularly safe, but the antihistamines I took were over the counter so it was no big deal...however, please ask your doctor first if it's OK to try this!