Yes, it could be done. OTL the negotiations to marry Isabel to Conde D'Eu started around 1860, but they only married in 1864, when she was 18.
Okay then, you've solved the age problem and now Maximilian can marry Isabel. They have a kid on the same schedule. I would think that Maximilian would probably get involved with the Brazilian navy, since he was a career naval officer. That has the added benefit of keeping him away from the disaster was that was the War of the Triple Alliance.
Well, the Republic was a conservative creation but with liberal support. The most liberal politicians, who believed that monarchies were an old fashioned regime (you can include in this definition all the positivists, who were the dominant faction among the young officers of the army, and the farmers from Western São Paulo, who founded the Republican party in 1870) joined forces with the conservatives (mostly farmers from East São Paulo, Rio and the Northeast). Neither the Church was supporting the Emperor, because of his support to the masonry. So, in 1889 the only supporters the Empire had were the rare monarchist liberals, as Joaquim Nabuco, who wanted a British system in Brazil, and the former slaves, that had no importance in politics.
Would the presence of the young Pedro d'Hapsburg, positivist army officer and Brazilian heir, make a difference in the calculus of the conservatives and their liberal allies?
Although you can't avoid the positivist influence in the army, if you get a quick victory in Paraguay you can avoid the Army becoming resentful of the Monarchy and the political system. So there would not exist the myth that "we saved the fatherland with our blood only, without support of Rio". Also, as Maximilian would not be involved in the war as Conde D'Eu (who was seen as an efeminate that never could even learn Portuguese), there would be less friction between the Monarchy and the Army.
I don't really think that I agree with this assessment. Although you may remove the mythos of the Army being the state that existed OTL, you won't remove the fact that the Army is going to become more and more involved in politics, and that the monarchy is going to be pissing the conservatives off with the slavery issue, and that the liberals really want a republic just on general principles. Now with the right kind of combination of personalities and a little bit of luck the monarchy can survive. The monarchy might be able to gain control of, or at least co-opt, the positivist influence in the army (with young Pedro), but I don't think that you'd be able to create a situation where Isabel and Pedro II survive the end of slavery. The monarchy, maybe with young Pedro, could survive.