UPDATE - I am restructuring my answer to better conform to the OP questions as suggested.
From the OP,
My question here is, is the Great Commission trying to make a
doctrinal point about baptism?
No, this verse is not making a "complete" doctrinal statement on Baptism. Although, it does conform and support the doctrine of believers baptism found elsewhere in scripture.
Is there anything being said about baptism, particularly infant baptism?
No. First, this verse isn't sufficient alone to make doctrinal statements about Baptism. Only doctrine you can draw from this verse about baptism is to support more detailed verses on baptism elsewhere. This verse does logically support believers baptism but when compared to other verses, one cannot make the leap from this verse to support infant baptism.
Does the Great Commission support Believer's Baptism since "making disciples" comes first?
Yes. As I have stated above, even if the Greek translates to a seemingly concurrent act, it still mentions "making disciples" first, then baptism, you can be sure of the doctrine by comparing to other scripture.
For example, believer's baptism is shown very clearly in Acts 8:35-38
35 Then Philip opened his mouth, and began at the same scripture, and
preached unto him Jesus.
36 And as they went on their way, they came unto a certain water: and
the eunuch said, See, here is water; what doth hinder me to be
37 And Philip said, If thou believest with all thine heart, thou
mayest. And he answered and said, I believe that Jesus Christ is the
Son of God.
38 And he commanded the chariot to stand still: and they went down
both into the water, both Philip and the eunuch; and he baptized him.
This is very clear that belief in Christ has to come before baptism. Baptism is a picture of the death, burial, and resurrection of Christ. It is a public profession of the inward change of the believer.
Thus, if the order for baptism in Mathew 28 can be seen and checked from other scripture, then you can easily have your answer to:
What are the doctrinal implications here, if any?
The answer is the verse alone cannot be used to form a complete doctrinal position on baptism but at the same time does not allow for infant baptism but does support believer's baptism.