It is only natural, when interacting with an alien species, to attempt to fit that species into the conceptual framework that we have developed- a framework that is limited by our own physiology. Our understanding of gender is a strictly binary, male/female point/counterpoint- and we do have some difficulty understanding other forms of sexual reproduction and, in most cases, attempt to fit that into our existing understanding of gender, even when such terms don't apply.
Gallifrean Time Lords may be aliens, but they certainly represent as passably human. Some incarnations of the Doctor (such as those played by Davidson and McCoy) look almost perfectly human, while others (Baker, Baker) bear only the most passing resemblance- but in all cases, we're dealing with a humanoid with roughly similar features- a creature that bears more resemblance to us than Neandertals. This is an amazing quirk of parallel evolution- we can assume then, that the environment of Gallifrey was very similar to that of Earth at some point in their evolutionary history. But not too similar- the resemblances are only skin deep.
While Gallifreans may have filled a similar niche, thus giving them gross features similar to our own, their physiology is signifigantly different- for one, we know that they have a binary circulatory system. An expensive prospect that had to develop in response to some external pressure- we may never know why. But a binary circulatory system implies an incredibly complex circulatory system, as well as a different structure of the nervous system- those two hearts need to be synchronized somehow.
Australia provides a good example of how even relatively similar species (in appearance) can have broadly different biology and methods of sexual reproduction- and in this case, I'm referring to marsupials. Marsupials in some cases mirror other species from other parts of the world- filling similar niches (for example, the fossil marsupial lion that was discovered) and thus having broadly similar appearance- but their sexual reproduction is vastly different. Now this demonstrates the differences that can form when a genetic population is isolated on its own continent. An alien from another world under a very different star and surrounded by entirely different creatures is sure to develop in a fashion very different from our own- despite the physical resemblance.
All in all, we do not actually know how sexual biology works with Gallifreans. We don't have enough information about them- but we do have more information. For example, the Doctor, aware of the cultural practices of humans, adopts a male demeanor, while Romana adopts a female. They assume these roles quite naturally, and it's clear that there are biological differences between the Doctor and Romana- consider her organs positioned similarly to human mammiaries. These biological differences carry across regenerations- which implies that those features are fairly important. While it is quite possible that these "mammiaries" are a racial, not a sexual difference, it seems unlikely. Very few features seem to persist across regenerations- those that do seem to be functional and structural- the Doctor is always humanoid, Romana always has "mammiaries". This leads me to conclude that those "mammiaries" are functional structures- although I have no evidence to that effect. Perhaps they are vestigal and unique to a subspecies of Gallifrean. Irregardless, the fact that she possessed them and the Doctor did not, that they persist across regenerations, denotes that there is a fundamental structural difference between the Doctor and Romana. If not a gender difference, it is a subspecies difference.
In fact, it does not matter. Based on the information that we have, there is nothing to indicate that the Doctor is male- or that such a term would apply even in a species with two variant genders. "Male" in our definition connotes the provider of sperm, while "female" denotes the source of eggs. We do not even know if "sperm" and "egg" apply to Gallifreans- it is entirely possible that they reproduce via budding. Unlikely, granted, but we have no direct evidence of their reproductive processes, but I propose that Gallifreans are post-reproductive, in that they do not reproduce in any conventional fashion.
My evidence for this is the regeneration process itself. A massive change to the body denotes what we would think of as a genetic alteration- and we gather from various conversations on the topic that this is not a purely biological process, but also a technological one. Very likely this was developed in conjunction with their Time Travel technology- but the mechanisms of such are beyond the scope of this essay. The fact that there is a limit to regenerations, and that the Master steals regenerations implies a technological aspect- these are reproducible events alloted to individuals. This requires a signifigant understanding of the underlying biology and most likely a complete restructuring of their biology. It is, in my mind, very likely that reproduction is carried out through a similar process. Judging from the different physiologies that are produced by the regeneration process, there does not seem to be a need to mix DNA- the primary goal of sexual reproduction. It seems just as likely that the Time Lords could create a new Gallifrean by simply flipping a switch and producing a new genetic sequence.
With this information, a new possibility for Romana's "mammiaries" becomes possible. We know that she was "younger" than the Doctor- perhaps, and this is pure speculation, her mammiaries were actually a generatated organ that facilitated the regeneration process. We know that the Doctor had several problems at various points with his regenerations, occasionally with serious dehabilitating effects (Colin Baker in specific). Perhaps Romana's "mammiaries" were a technological adaptation to the regeneration process, not a sexual or subspecies feature.
In conclusion, we do not have much information about sexuality among the Time Lords. While the Doctor presents himself in a fashion that leads us to think of him as male, and Romana lead humans to think of her as female, it is doubtful that any such distinction can honestly be made. Given what we know of their control over their own biology, it is unlikely that any such distinction would be truly meaningful. If we ever see a pregnant Time Lord (unlikely, since all but one Time Lord is deceased, and it is unlikely that the Doctor could reproduce with an alien), perhaps we might be able to revise this. I do not think that we ever would see a pregnant Time Lord, because I do not believe that they would gestate an infant when their technology allows for a far more effecient process.
I put too much effort into this. I know.
/me is a giant nerd.