Is it Adventurers League legal for a halfling ranger to use the Pteranodon as an animal companion in Eberron where halflings routinely ride dinosaurs?
Yes, per RAW a ranger can have pteranodon as his/her animal companion.
The two prerequisites for a ranger's animal companion are (PHB page 93):
"... a beast that is no larger than Medium [emphasis mine] and has a challenge rating [CR] of 1/4 [emphasis mine] or lower..."
A pteranodon satisfies both of those requirements.
Also relevant to address the AL part of your question is this quote from the AL FAQ v8.2 on page 6:
Creatures with complete stat blocks found in the Monster Manual and other resources listed in the ALCC are available for use with class features such as Wild Shape, Beast Companion [emphasis mine], and various conjure spells, keeping in mind that your Dungeon Master is the final arbiter for the rules, such as determining whether or not your character has satisfied requirements such as those imposed upon you by your class (such as the druid’s requirement to have seen the beast in question).
Per this reference, you may certainly use the Monster Manual as a legal resource and the pteranodon from it as your companion. It would also appear that there are no class requirements imposed by the ranger's Beast Companion ability that you must meet to select it.