Taken in the sense of “the act of teaching” and “the knowledge imparted by teaching”, this term is synonymous with CATECHESIS and CATECHISM. Didaskalia, didache, in the Vulgate, doctrina, are often used in the New Testament, especially in the Pastoral Epistles. As we might expect, the Apostle insists upon “doctrine” as one of the most important duties of a bishop (1 Timothy 4:13, 16; 5:17; 2 Timothy 4:2, etc.). Cf. Catholic Encyclopedia > D > Christian Doctrine
or truths having a necessary connection with these[i] become formally dogmas when defined and proposed by the Church.
CCC 88 The Church’s Magisterium exercises the authority it holds from Christ to the fullest extent when it defines dogmas, that is, when it proposes, in a form obliging the Christian people to an irrevocable adherence of faith, truths contained in divine Revelation or also when it proposes, in a definitive way, truths having a necessary connection with these. Cf. Catholic Encyclopedia > D > Dogma
In general, infallibility is exemption or immunity from liability to error or failure; in particular in theological usage, as regards the Church, it is the supernatural prerogative by which the Church of Christ is, by a special Divine assistance, preserved from liability to error when and in what she teaches a doctrine of faith or morals. Cf. A Primer on the Infallibility of the Catholic Church
(not subject to revision or alteration – irreformable dogma – Merriam-Webster)
This is a quality/characteristic of a dogma
And this infallibility with which the Divine Redeemer willed His Church to be endowed in defining doctrine of faith and morals, extends as far as the deposit of Revelation extends, which must be religiously guarded and faithfully expounded. And this is the infallibility which the Roman Pontiff, the head of the college of bishops, enjoys in virtue of his office, when, as the supreme shepherd and teacher of all the faithful, who confirms his brethren in their faith, by a definitive act he proclaims a doctrine of faith or morals. And therefore his definitions, of themselves, and not from the consent of the Church, are justly styled irreformable, since they are pronounced with the assistance of the Holy Spirit, promised to him in blessed Peter, and therefore they need no approval of others, nor do they allow an appeal to any other judgment. For then the Roman Pontiff is not pronouncing judgment as a private person, but as the supreme teacher of the universal Church, in whom the charism of infallibility of the Church itself is individually present, he is expounding or defending a doctrine of Catholic faith. The infallibility promised to the Church resides also in the body of Bishops, when that body exercises the supreme magisterium with the successor of Peter. To these definitions the assent of the Church can never be wanting, on account of the activity of that same Holy Spirit, by which the whole flock of Christ is preserved and progresses in unity of faith. (My emphasis) (LG, 25)
As regards Church Teaching, both infallibility and irreformability are characteristics of dogmas of the Church but from the definitions above, infallibility does not equal irreformability.