Okay, now I'm going to have to put on my professor hat.
An "apples to oranges" comparison is comparing two things that are fundamentally incomparable. For example, the chance of dying in an earthquake vs. the chance of dying on a flight. One is expressed in units of time, the other is expressed in units of distance. These two numbers are not directly comparable, and never will be unless you make assumptions about how many miles per year one flies, converting a distance-based unit to a time-based one.
Two probabilities expressed in the same units (per-passenger-mile in this case) are absolutely NOT an apples to oranges comparison, no matter how many times you choose to repeat the phrase in your "argument."
As for where to find the statistics, it's not that hard when you are properly motivated. Now that I'm properly motivated, here is a good place to start:
http://www.faa.gov/passengers/images/MedArticle.pdf
This is a paper that was published in a peer-reviewed journal of pediatric/adolescent medicine. The executive summary of that article (and it's the first link returned from a google search on the terms "unrestrained infant injury passenger mile FAA"): cars are so much more dangerous than airplanes that *requiring* families to pay a non-trivial amount to get a seat for their children may well cause enough families to drive instead of fly (for economic reasons) resulting in
more dead children overall. You don't need to agree with this study---I certainly read peer-reviewd articles in my own specialty which I think are flawed---and it's conclusion is certainly counterintuitive. But, I think it would be wrong to simply dismiss it out of hand.
Plus, it conveniently collects the relevant fatality rates for us in one place.
The next several links returned by this google search are all news releases touting this 2003 article, and so don't add much to the conversation. The next relevant document in the returned list is a study available on NASA's site.
http://techreports.larc.nasa.gov/ltrs/PDF/2001/mtg/NASA-2001-aasce-aeg.pdf
It's not clear to me whether this was a peer-reviewed article, but it is listed as copyright by SAE, so I'm assuming it was probably in one of their journals. It rightly points out that, all other things being equal, properly restraining a child increases that child's chances of survival. It also has lots of good data on injury and fatality across a broad spectrum of events and passengers.
However, this paper also cites a different study undertaken by the FAA which suggests that even approved restraining devices may not help all that much. This paper can be found here:
http://www.cami.jccbi.gov/AAM-400A/Abstracts/1994/FULL TEXT/AM94-19.pdf
It was published in 1994, so one can safely assume that there have been design changes in approved seats (and even possibly changes in the FAA approval criteria) that improve matters, perhaps substantially. And, I would say that the characterization of this paper by the NASA study with respect to the performance of safety seats was overly simplistic. However, the conclusion of this '94 study (on pages 27 and 28) is simple: *only* aft-facing child seats provide any substantial protection. Forward-facing seats designed for automobiles do not work, because the inter-row distance, seat construction, and seat belt design on an airplane are substantially different from that in an automobile. Furthermore, toddlers (two years and up) fare *better* in the plain lap belt than they do in forward-facing seats on an airplane. This paper is also clear on the point that lap-held children are not afforded any reasonable protection in a crash.
That said, this paper has a conclusion interesting enough to warrant including it here (again, on page 28):
These conclusions should not be construed as an indication that a dangerous condition exists for children traveling in commercial transport airplanes. The accident rate for commercial operations in 1991 was 0.32 per 100,000 departures, which affirms the fact that commercial aviation is a very safe mode of transportation. Rather, this information is presented to identify a particular component of passenger safety, child restraints, which may not meet the expected levels of performance in an accident.
Even considering this is an FAA-generated report, and the FAA's job is to make people feel good about flying (much as the TSA's job is to make people feel safe about flying rather than to necessarily make flying safe), that's still an interesting conclusion.