Unfortunately, this series seems to be in a bit of a decline, at least for me as a reader.
I read fantasy voraciously, and I'm normally a huge fan of fiction (historical and otherwise) set in this era, from Jane Austen to Patrick O'Brian's Aubrey/Maturin novels, etc.
The first novel in this series, His Majesty's Dragon (Temeraire, Book 1), I really enjoyed and respected -- it managed to mix fantasy elements with the historical setting in a way seemed believable and real. The most difficult thing to do in historical fiction, and especially in cross-genre historical fiction/fantasy, is to make the novel "come to life" *in the historical setting* ( a trick that only a rare few other authors have managed), to make the book read like an authentic period account.
The problem, as this series has continued, is that the character's actions have lost their ground -- I no longer feel like I'm reading a story with characters who were alive in the 18th and 19th centuries. I feel like I'm reading a story that has a bunch of modern characters in fancy dress. The moral decisions the characters make are based on modern values and modern frameworks, not period ones; the political concerns that appear to drive these later novels ( "what if dragons had meant there wasn't any imperialism or colonialism?")are concerns that almost continually force the reminder that the books are written by a modern author.
This latest volume continues that trend. The human characters just don't seem to act in a way that comes across as a realistic representation of british officers from that era -- they come across instead (the lead human character especially) as a modern individual in a period uniform. By this point in the series -- transported to Australia and finding themselves at odds with even those there as well -- he's coming very close to rejecting the worldview and value-system of his entire society, in a way that just isn't realistically believable, at least to this reader.
If that lack of period voice doesn't bother you, though, you might find this book entertaining enough. Be prepared for a plot that's a fair bit "girlier" (for lack of a better term) than the earlier novels -- the dragons seem to spend a much greater amount of time worrying about what they and their handlers are wearing, for example, than actually getting into battles of any kind, and most of the drama and tension in the novel involves a lost dragon egg. But if the above concerns aren't a problem for you, and you liked the last few books, you might find it worth reading this one as well, just to continue the story.
EDIT: After thinking about this for a while -- I really did *want* to like this book -- I think a large part of my dissatisfaction might be due to this series having made a subtle genre shift, from "historical fiction" to "alternate history" (if that distinction makes sense). The first few books were set in, and bound by, and "real" within the context of, a specific historical era (Regency/Napoleonic). By this point in the series, however, things have veered so far away from that setting -- not just in terms of historical events, but also in terms of the primary character's own mental landscapes -- that, for me at least, that sense of "reality" and believability has been lost. This may be my own personal flaw as a reader, and it may seem a silly criticism to level against a book with, you know, Dragons in, but whatever the cause, this series just isn't as enjoyable for me as it was initially. If you're more a fan of alternate history than I am, you might like this.