Is this quote grammatically correct?

Nature thought beauty too rich to go forth upon the earth without a meet alloy.

Several words here are omitted for style. Restoring them we get:

Nature thought [that] beauty [was] too rich to go forth upon the earth without a meet alloy.

The key ideas here are:

rich is used metaphorically, to indicate that beauty is too wonderful and powerful to leave alone.

to go forth upon the earth is just a poetic way of saying "to go out" or "to go free".

meet here is an adjective (not a verb!) that means "fitting" or "suitable". This usage of the word "meet" is very archaic and poetic.

alloy is used metaphorically as well, to mean something like "companion".

So a colloquial translation would be something like "Nature thought beauty was too great to be let out alone without something to accompany it."

meet adj.

precisely adapted to a particular situation, need, or circumstance : very proper

alloy n. (4th definition)

a compound, mixture, or union of different things <an ethnic alloy of many peoples>

So a "meet alloy" would mean a "very proper union":

Nature thought beauty too rich to go forth upon the earth without a very proper mixture

It's grammatically correct. But the structure of the sentence seems to specify that the alloy is possessed by beauty, which would be incorrect, since an alloy refers to the combination itself — including "beauty". Companion or a similar word seems to fit better.

Instead of this being incorrect though, I more think that the author meant to imply that the alloy was to be provided alongside, not possessed, by beauty.

In this case 'meet' is not a verb it is an archaic adjective for expressing 'fitting'.

Meet: archaic proper, fitting, or correct

An alloy is a mixture of two metals, usually with one being of lesser value.

In others words, "beauty was too powerful to go into the world without another baser element to corrupt it." (beauty would just be too attractive without a downside.)