I typically associate bucklers with Medieval warfare manuals, so when I first came upon this passage, I assumed that it was an anachronistic reference, but Robert Alter's translation also uses buckler, which makes me wonder if there was indeed a use for bucklers in ANE fighting. I find this fascinating, considering that ANE warfare is usually depicted with large shields. Any insight here would be much appreciated!
Buckler is probably a poor translation. The two Hebrew words are מָגֵן (magen) and צִנָּה (tsinah). Both are translated as "shield" and "buckler" in various places in common translations of the Bible. In the text from Psalm 35:2 you quote, "magen" is translated as "shield", and "tsinah" as "buckler". However, a "tsinah" appears to be a very large shield - a pavise that is carried by a shield-bearer, and protects the whole body. A "magen" is a conventional shield, worn on the forearm or carried in the fist, depending on whether it is forearm-strapped or centre-grip.
Rather than "shield and buckler", "shield and pavise" appears to be a more accurate translation.
The etymology of tsinah is obscure. It appears to come from a word meaning "thorn", perhaps via an intermediate word for a protective thorny hedge.