About the "Dorothy". It sailed from Plymouth in March 1849. ...If you google: "Ship - Dorothy - 1849" a few things come up on the list which might be of interest to you.
The first item tells you in detail all about the conditions on the "Dorothy," which were apparently very good.
6th from the top of the list is a site marked "1849" That one mentions the passengers, but only William Williams and Maria. It doesn't seem to mention the son William, which is a big puzzle.
I tried Ancestry's Ships Passenger Lists, UK to Victoria, for the "Dorothy", but the ships passenger list didn't come up there.
There are baptismal & Christening lists for London on Ancestry. In theory, the birth should be there.