Edit: i am assuming modern as in "available today" technology.
Let us see. Let's estimate the parameters first.
How long does the cruise take?
A modern cargo ship (according to Wikipedia) goes 21-25 knots. That's roughly 21-28 miles per hour, let's go with 25, because i am lazy. Since i used to sail the oceans myself when i was younger, i do know that currents can reduce that speed to 0 or less (relative to sea ground) when strong currents are involved. Let's assume your ocean has strong currents that, over the course of the journey, cancel each other out. But keep it in mind if you want to make the journey interesting (or prolong or shorten it).
25 miles per hour means 600 miles per day (ships need no sleep), that's 417 days of travel.
How much food and supplies are being consumed during that time?
An average human requires 3x400g of food per day, that's roughly 1,2kg. Getting supplies that last 400 days is not a problem. Since we have 10,000 people, they consume 12000kg, or 12 tons of food per day. That's an impressive 5004 (metric) tons of food during the travel. But hold - they also require fresh water. 2 Liters per day per person. That's another 8340 metric tons of supplies, adding up to a total of 13344 tons of supplies (just food and water).
How much can a modern cargo ship handle?
The Barzan (Wikipedia) can handle up to 200.000 tons of dead weight...
How many passengers can a ship carry?
The Queen Mary 2 has a little bit more than 4000 people on board (Wikipedia)
So how many ships does our fleet need?
You need 4. A cargoship for food and supplies, a ship carrying the fuel (i suppose the cargoship will also carry 150.000 tons of colony supplies, clothing and all that stuff), and 2 cruise liners, providing a year worth of entertainment for our colonists.
You might want to build 4 identical ships, each carrying a part of crew, cargo, supplies and enough fuel, so you don't risk killing everyone by losing a single ship.
So how difficult is this?
Not at all. More like a nice, chill cruise :) And it's not even expensive...