Probably not
You'd need so many other passages to support the idea that this passage wouldn't add much. So, Theology about Jesus's deity should come from other passages. That's how Bible Hermeneutics apply to development of theology.
At most, you could say that this is "consistent" with Jesus' identity with the Father. But, then you would need to explain why Jesus isn't setting an example for Paul to follow.
Paul also calls people "son"
To say that this indicates Jesus's divinity with the Father, you would need to explain how Paul is not making the same claim. For example, you would need to quote Paul from his same reference saying something like, "...in a different way from Christ," but he doesn't say things like that.
1 Timothy 1:2 (NASB)
To Timothy, my true son in the faith: Grace, mercy, and peace from God the Father and Christ Jesus our Lord.
Philemon 10 (NASB)
I appeal to you for my son Onesimus, whom I fathered in my imprisonment,
Titus 1:4 (NASB)
To Titus, my true son in a common faith: Grace and peace from God the Father and Christ Jesus our Savior.
...Note the use of "in a common faith", possibly taken "according to" because of the noun case in Greek—same basic idea.
John addresses people as "little children"
1 John 2:12 (NASB)
I am writing to you, little children, because your sins have been forgiven you on account of His name.
It seems that John and Paul are following Jesus's example.
Jesus sets an example of family in faith
Jesus, John, and Paul all do this in reference to people who believe. That common ground indicates that they are acting with an "adoption" attitude, to let people know that they are part of a kind of family.
Apply the result of our hermeneutics to guide our hermeneutics
If we take this to mean "Jesus is therefore God", that would remove Jesus as an example in how Christians can treat each other like family.
It may seem strange to us for people to talk this way, but it didn't seem strange to the New Testament community. Those people seem to have felt "included" and "adopted" when Jesus, Paul, and John talked this way. They didn't start bolstering a Trinitarian theology. I believe in the Trinity, but not because of Jesus kindly calling someone "daughter".
When I read Jesus, John, and Paul doing this, I learn that I need to talk to people with more love.
A Trinitarian Theology should come before this and offer insight on this, not be built from this.
If one believes that theology, as I do, we couldd say, "Jesus says this as God including us as family, which we already know from other passages. Paul and John follow the same example in their own capacity, just as we all can treat each other as family."
In other words, Christians should love each other more. The application that comes after hermeneutics would be a critique on society today. So many people claim to believe in this Jesus you quote, but use theology and other differences as excuses to fight rather than as excuses to love, accept, and adopt. They misunderstand the purpose of Jesus's words.
Further reading
Another writer, Steve Shirley, has some good thoughts:
This being said, there are two explanations given. The primary one, given by most, is that Paul led Timothy to saving faith in Christ.
However, there are also some who believe that Paul may have called Timothy his “son” simply because he was kind of like an “apprentice” to Paul.
