What kind of vessel is suitable for storing and aging eggnog?
When in doubt, look at how the professionals do it: Use the vodka bottle that'll be empty by the time the eggnog is ready to be poured into a container.

Jam jars are easier if you don't have a funnel handy, but depending how much of an alcoholic you are on the alcohol content of your eggnog, you could use the proverbial chalice found in the basement of your castle and just give it a fast wipe-down with a 100 year cloth as it contains so much alcohol it'll sterilise said chalice.

Personally, I use my left-over eggnog to strip paint off walls.  ;-) 0:-)