How to use 得 without single-character verbs (e.g. 我旅行得很快)?
I would say that "A得B"(述语+补语) form does not add constraint on the number of characters of either A or B. But if encountering a choice between "学得快" and "学习得快" in oral language, most native speakers would select the former one since it's shorter, although both of them are correct from the view of grammar.

For the case of "旅行得很快", I don't think it's incorrect in grammar. If you have a reasonable context, it can also appear in oral language, although people would prefer saying "旅游" or "玩" to "旅行" (which sound too formal, like written language). Since people would not often talking about how fast their travelling is, many people may think this odd.

Moreover, although "学" and "学习" can be used as both noun and verb. In most cases orally, "学" uses as verb and "学习" as noun.

Some more examples of "A得B" form with more than one character in A:


这个项目计划得很周密。

This project plans thoroughly.
他高兴得眼泪都流出来了。

He is happy into tears.
这首歌要好听得多。

This song is much better.