Is this sentence correct?
Yes, your sentence is perfectly correct.
and
Is there another meaning that makes sense that I don't know?
Yes, there are many meanings of する suru (Wiktionary).
Your sentence falls under definition 11.
From the link:
11（修飾語 + 体の一部 + をする）その人の特徴として、そのようなものを持つ。
青い目をした少女。
あの子は長い髪をしている。
Translated:
11 (Following the adjective + noun + case-marking particle を,) the word (actually it is the continuative form of する → し) denotes the characteristic of the person related.
Example 1: The little girl has blue eyes.
Example 2: The girl? child? has the long hair.
Here the adjective is 小さい, in English 'small', and the referenced noun (before し) is 口元, in English, 'mouth'.
P.S Regarding the bold marked case-making particle を, it would be hard for the Japanese learners to comprehend ( I guess ) why it should be there so that I would like to explain for further information. Japanese sentence has the structure of 係り受け（かかりうけ）, which means, the former "parts of speech", here, その少女は小さい口元を, "continuously modifies" the latter parts of the speech, in this case, している, especially the verb し, which means here, "looks like", "seems...". The examples are here.
状態動詞(じょうたいどうし）の現在形（げんざいけい）：
① 現在（げんざい）の一定（いってい）した状態（じょうたい）
次(つぎ）も状態動詞（じょうたいどうし）です。
「～ のようすをしている」
Translated
The progressive form of the substantive verb
①( Expressing ) the continuous state, or the condition, or the appearance ( in your case ), ( of something or somebody )
The next is too the example of the speech using the substantive verb.
It seems 〜
Let's switch the word using the above example so that you might be able to understand more precisely.
のようすをしている --> Swap the ようす（様子） by 口元
then
の口元をしている。
But this does not YET matches with your former part of the speech.
What is the difference then?
It is not so hard. Since 口元, mouth is a noun, in your case the adjective 小さな should be in place of の of the above example.
の口元をしている
-->
小さな口元をしている。
Translated ( in your case )
(The girl) seems to have the little mouth ( Though the translation is weird. )
Why I dared to use the word seems is just only to emphasize the verb する, or し ( continuative form ) of your case, denotes the "appearance" or the "condition" ( of the girl ).
I hope you were able to understand by my flimsy English....
Translated
FYI
If you would like to know the grammatical structure of している, it can be broken into parts of speech as the following:
し the continuative form of する
て conjunctive particle, meaning, after the て follows something.
いる stative verb, equivalent to English's be, and the form is conclusive.
Have a nice day.
