I hope that by '1800s' you mean 19th century, not only the first decade of it, as the following addresses almost whole century.

In the beginning of the 19th century, the speed of an average merchant ships used for transoceanic trade, such as British Indiamen was in the ballpark of 4 knots, i.e. 4 nautical miles per hour. As the ship was able to travel around the clock provided good conditions, this meant that such ship was able to cover 96 nautical miles or 110 land miles within 24 hours. Clippers, arguably fastest transocceanic merchant ships of the 19th century were very fast in comparison, capable of pulling 7-8 knots on regular basis. The distance of 16000 nm between Fuzhou and London has been covered in 99 days during the Great Tea Race of 1866 and in 90 days by American clipper 'Witch of the Wave' in 1852. Just remember that we're speaking of loaded merchant sailships here carrying roughly 500 tons of cargo.

Since the early 1830's ships started to use steam engines as an auxiliary and then main then the only power source. These required a network of coaling stations along the route to operate with maximum efficiency, but were still pretty fast and, what is more important, largely independent of the winds. Average speed of 'Great Western', steam and sail ship built in 1837 was in the ballpark of 11 knots (488 km or 305 miles per day). Average time of travel on the Liverpool-New York route was 12 days, although this was considered quick travel, as most ships of the this decade could muster 8-9 knots tops (thus lengthening the cross-Atlantic travel to 17-18 days. 'Great Britain', the first ship with an iron hull and screw propeller (along with six masts) had an average speed of 12-12.5 knots. Same was true for the French battleship 'Le Napoleon' launched in 1850.

Nellie Bly, an American journalist, inspired by Jules Verne's 'In 80 days around the world' took a similar trying to beat the Fogg's challenge in 1888. She left detailed notes from this journey (finished in 72 days) that are a good source for the data relevant to your question. For example, New York-Southampton stage by Hamburg America Line took 7 days (3150 nm, what gives us roughly 18 kn); Brindisi-Colombo by P&O line (4410 miles, via Suez) took 16 days, what gives us 11.5 kn. Hong Kong-Yokohama stage was similar (1600 nm in 5,5 days, what gives 12.5 knots on average), same for Yokohama-San Francisco (4500 nm in 15 days, i.e. 13.5 kn on average). So, you can safely assume that in the 1888/1889, average speed of a passenger ship was roughly 12-14 knots with state of the art vessels being capable of travelling almost half as fast.