I've carried children in front and rear bike seats, in trailers, and on trailer bikes for over seven years now. And 7 years is the length of time I've been using our trailer.
Be assured that drivers give you far more room than they do when you're just on a bike. They are far more visible than a bike. If the bike goes over, the trailer doesn't, so there are other safety advantages.
If you want to get a helmet for your daughter for a bike seat then fair enough. But there's really no need to get defensive when asking for advice on a forum full of cyclists with experience of the subject you're asking about.
And I've got no children, but I've worked a lot with promoting cycling to the public, including families, and I'd agree with what Paul says. Trailers are very safe, and very noticable. A driver who didn't notice one is likely to not notice you either, frankly. You get much more room when towing one (I have done - it happened to be full of shopping, it was great, loads of space from people passing). And they are a roll cage - if the kid is strapped in properly, the trailer could turn right over and the kid will be ok - a bit surpised, but ok. However in normal road use, I've never seen one tip over.
As for the exhaust fumes, she'll get more exhaust fumes inside a car than in a trailer, even if she is nearer the pipes. And think about it. In traffic, you'll be pulling up behind cars (not much chance to filter with a trailer on). The trailer will be behind you, more than a bike length away from the exhaust pipe in front and more than a car's length from the exhaust behind. And while moving, the throughput of air will mean she breathes the same air as she would in a seat.
If you can't find a helmet big enough, I'm afraid it's probably for exactly the reason people have said - you're not meant to be needing one for her at that age.
