Is it safe for a dough containing egg to rest at room temperature for more than 2 hours?

Well the FDA says dough with eggs can rise up to two hours, and after that should be refrigerated. However, me and a great many others routinely do proof enriched doughs at room temperature for time that exceed that. The bacteria you are most likely concerned about is probably salmonella. That is killed off when internal temps rise to about 165F. Your bread is going to be baked until it is in the area of 190F to 210F, which will have long since killed off any gerbies. I would point out that bread has been made for hundreds and hundreds of years, most of which time there were no refrigerators. Folks died of lots of things, but I kind of doubt bacteria from their bread was the cause. The US is also one of the few countries that routinely refrigerates eggs as well. If you are really nervous about this, you can certainly do a very long proof period in your refrigerator, and then allow the risen dough to warm up before the final bake. I don't think it's necessary, but if it eases your mind, then do it.