Learn English – a word for wanting to be somewhere else

It is also called a serving hatch.

An opening in a wall at window height for the purpose of serving food or other items.

The cook passed the dishes through the serving hatch.

from Wiktionary

As @Jeremy says, straight-up anxiety is a normal term for this context. Apprehension is similar but perhaps sometimes less forceful. I rather doubt English has any particular words that are especially associated with the anxiety that immediately precedes a long trip.

I don't think travel anxiety is particularly apt, to be honest. It's more likely to be interpreted as anxiety about the impending journey (travelling alone, fear of flying, worry about missing connecting trains/flights, etc.). OP specifically mentions "preemptive homesickness" as relevant, so we should assume the journey itself it not the focus of the anxiety.

It's not just metaphoric that many relevant expressions can also be used of an upset stomach. States of acute anxiety do often noticeably disturb internal visceral processes in this way. I therefore suggest OP gets the collywobbles, or has butterflies in his stomach. Both these expressions will ordinarily be interpreted as more forceful than simple anxiety.