No simple answer I'm afraid and in the end the birth may not be recorded in any document anywhere.
HMS Victory did indeed go to Lisbon in 1811 as flag ship of Rear Admiral M Dixon, under the command of Captain G Honey. The problem could not only be in identifying all the other ships that accompanied her, but knowing in what capacity her parents were travelling. Army, Navy, Government Official or in some civilian capacity. Then there would be other merchant vessels that would have gone there also.
Births to wives of army personnel have been recorded in Regimental and/or Chaplains returns from 1761 and if your Brymer ancestor's father was in the army, there was a chance the birth would have been recorded in army returns once they reached land. Army returns are now online at the 1837online web site, I've checked for Brymer and Brimer, but unfortunately the birth does not appear to be recorded.
Although births at sea were not formally recorded until 1837 and much later for Royal Navy ships, some births on Royal Navy vessels have been recorded in ships logs [the earliest in the late 1700's], many ships logs are in the National Archive, Kew in documents series ADM 53. As I pointed out earlier, without knowing the one in which her parents were travelling, you will need to identify all likely ships. It will be a long trawl but that could be done checking ships listed in "Ships of the Old Navy" in part 1 of the Maritime and Naval History web site [see below].
One other possibility is the Consular papers, again recording births in Consular returns was not made compulsory until 1849, but there is a chance the birth was recorded. A search of the National Archive [www.catalogue.nationalarchives.gov.uk ] catalogue [PROCAT] using the word births, dates 1800-1820 revealed there is a birth register for the British Consulate in Portugal in Piece FO559/1:Foreign Office: Consulate, Ponta Delgada, Portugal: Miscellanea; Register of Births, Deaths, Baptisms, Marriages and Burials; covering dates: 1807 Jan.6-1866 Mar.12
Unless you can get to the National Archive, Kew, in person you are likely to need to use a private researcher. I think the cheapest option is to eliminate the FO559/1 document first and there are two companies that may help. Have a look at Research-UK at http://www.research-uk.co.uk/http://www.research-uk.co.uk/ and A & H Associates athttp://www.aha.ndirect.co.uk/http://www.aha.ndirect.co.uk/, these are private companies specialising in BMD and other searches at the PRO, but you will have to make it clear what you seek and they are likely to charge at the hourly rate [it will still be cheaper than the NA's rate.], so email them for an estimate.