The etymology of the word "pedophile" as I know it is fraught with peril. As I recall it, the word should be spelled and pronounced as pædophile.
In print, you can see the word paedophile in the Collins English Dictionary – Complete and Unabridged, 12th Edition. The paedophile spelling goes back as far as 1908, whereas the pedophile spelling only started appearing in 1944 according to the Google Ngrams library. It looks like the word was just too difficult to properly enunciate for most people, so the spelling was changed to reflect the common pronunciation when it started becoming popularized amongst the general public.
However those ae/æ words have been seemingly evicted from the language. Yeah, the Encyclopædia Britanica still uses the Encyclopædia spelling and have been since at least the 9th edition which is significant but as far as I know everybody else, including the now much more known Wikipedia, the free Encyclopedia uses the alternate spelling. The Google nGrams are pretty condemning here too as the Encyclopædia spelling has been declining in isolation from the other variants and isn't even a blip on the radar by means of comparison if you discount what's arguably the most significant historical use of the word.
Do note that this makes so much more sense with The Online Etymology Dictionary etymology entry Silenus already mentioned:
1900, from Greek pais (genitive paidos) "child" (see pedo-) + philos "loving" see -phile). First attested in an abstract of a report by Krafft-Ebing.
The emphasis is my own, to emphasize the probable pronunciation of the word-forming element we probably should be using, if people weren't lazy and the cause wasn't hopeless. Oh well, at least it's not like pedophile ever meant anything else in English as far as I know, although it does seem to deny foot fetishists the unique single word they should rightfully own (which is not to say that anybody would want the name at this point anyway). Regardless, if not only in order to further emphasize this point, let's go look at the referenced entry at The Online Etymology Dictionary too:
Pedo before vowels ped-, word-forming element meaning "boy, child," from Greek pedo-, comb. form of pais "boy, child," especially a son, from PIE root *peu- "small, little, few, young" (see few (adj.)). The British form paed- is better because it avoids confusion with ped-.
paedo- see pedo-.
A recent use of the word can be found in Stop Using the Word Paedophile, written
by Julie Bindel for The Guardian.
Citations and Alternate links:
Wiktionary entries for pædophile and encyclopædia, reproduced on Wordnik.
The Collins English Dictionary – Complete and Unabridged, 12th Edition's entry for paedophile.
As stated by Stop Using the Word Paedophile, written
by Julie Bindel for The Guardian and published Tuesday 23 May 2006: Archived on The Internet Archive's Wayback Machine
This is the present Encyclopædia Britanica's homepage, archived on The Internet Archive's Wayback Machine
There is a photograph on The Dull but Dependable Encyclopaedia Britannica Bows to the Digital Facts of Life by Max Davidson for The Telegraph 14 Mar 2012, archived on The Internet Archive's Wayback Machine
This is Wikipedia Homepage, 31 Mar 01 snapshot, archived on The Internet Archive's Wayback Machine
This is a Screenshot of the Google Ngrams Usage Trends Comparison for, Encyclopaedia, Encyclopædia and encyclopedia.
This is Screenshot of the Google Ngrams Usage Trends Comparison for Paedophile, Pedophile
This is a Google nGrams Screenshot for the usage trend of Encyclopædia, which is isolated from other words
This is The Online Etymology Dictionary's Entry for pedophile: Archived on The Internet Archive's Wayback Machine
This is The Online Etymology Search Results Page for pedo-, with the paedo wordforming element
Here are scholarly citations for The Online Etymology Dictionary, and an archival link to them The Internet Archive's wayback machine.