Looked on the cunard site. No world cruise for QM2 yet. QE2 just started one. And you can do it for $24,000.
http://www.cunard.com/CruiseItinerary.asp?cruiseid=2498&LeftNav=Planner&Active=&Sub=&OB=&Region= Voyage of the Explorers III
Queen Elizabeth 2 · 104 Days
Fares From: $23,999
January 2004
5 Mon New York, NY, USA Depart 4:45 pm
6 Tue Cruising the Atlantic Ocean
7 Wed Fort Lauderdale, FL, USA 8:00 am - 5:00 pm
8 Thu Cruising the Great Bahama Bank, USA
9 Fri Cruising Caribbean Sea
10 Sat Cartagena, Colombia 8:00 am - 5:00 pm
11 Sun Transiting the Panama Canal, Fuerte Amador, Panama 6:30 am - 11:59 pm
12 Mon Fuerte Amador, Panama 8:00 am - 6:00 pm
13 Tue Cruising Pacific Ocean
14 Wed Cruising Pacific Ocean
15 Thu Acapulco, Mexico 8:00 am - 6:00 pm
16 Fri Cruising Pacific Ocean
17 Sat Cabo San Lucas, Mexico 8:00 am - 6:00 pm
18 Sun Cruising Pacific Ocean
19 Mon Los Angeles, CA, USA 8:00 am - 10:00 pm
20 Tue Cruising Pacific Ocean
21 Wed Cruising Pacific Ocean
22 Thu Cruising Pacific Ocean
23 Fri Honolulu, Hawaii, USA Arrive 2:00 pm
24 Sat Honolulu, Hawaii, USA Depart 6:00 pm
25 Sun Cruising Pacific Ocean
26 Mon Cruising Pacific Ocean
27 Tue Cruising Pacific Ocean
28 Wed Pago Pago, American Samoa, USA 1:00 pm - 6:00 pm
29 Thu Cruising Pacific Ocean
30 Fri Cross International Dateline - Lost Day
31 Sat Lautoka, Fiji 7:00 am - 6:00 pm
February 2004
1 Sun Cruising Pacific Ocean
2 Mon Noumea, New Caledonia 8:00 am - 4:00 pm
3 Tue Cruising Pacific Ocean
4 Wed Russel, Bay of Islands, New Zealand 9:00 am - 6:00 pm
5 Thu Auckland, New Zealand Arrive 7:00 am
6 Fri Auckland, New Zealand Depart 10:00 pm
7 Sat Cruising the Southern Ocean
8 Sun Wellington, New Zealand 7:00 am - 8:00 pm
9 Mon Lyttelton, New Zealand 8:00 am - 6:00 pm
10 Tue Snares Islands, New Zealand Arrive 1:00 pm
11 Wed Cruising the Tasman Sea
12 Thu Hobart, Tasmania, Australia 8:00 am - 5:00 pm
13 Fri Melbourne, Australia Arrive 5:00 pm
14 Sat Melbourne, Australia Depart 6:00 pm
15 Sun Cruising the Tasman Sea
16 Mon Sydney, Australia Arrive 6:00 am
17 Tue Sydney, Australia
18 Wed Sydney, Australia Depart 6:30 pm
19 Thu Cruising the Great Barrier Reef
20 Fri Cruising the Great Barrier Reef
21 Sat Yorkeys' Knob Marina (Cairns), Australia 7:30 am - 6:00 pm
22 Sun Cruising the Coral Sea
23 Mon Cruising the Solomon Sea
24 Tue Lae, Papua New Guinea 8:00 am - 6:00 pm
25 Wed Cruising the Bismarck Sea
26 Thu Cruising Pacific Ocean
27 Fri Apra, Guam, US 8:00 am - 6:00 pm
28 Sat Cruising Pacific Ocean
29 Sun Cruising Pacific Ocean
March 2004
1 Mon Yokohama, Japan 8:00 am - 6:00 pm
2 Tue Cruising Pacific Ocean Arrive 12:00 am
3 Wed Kagoshima, Japan 8:00 am - 6:00 pm
4 Thu Cruising the East China Sea
5 Fri Keelung (Taipei), Taiwan 8:00 am - 6:00 pm
6 Sat Cruising the South China Sea
7 Sun Hong Kong, China Arrive 8:00 am
8 Mon Hong Kong, China
9 Tue Hong Kong, China Depart 6:00 pm
10 Wed Cruising the South China Sea
11 Thu Cruising the Gulf of Thailand
12 Fri Laem Chabang, Thailand Arrive 8:00 am
13 Sat Laem Chabang, Thailand Depart 7:00 pm
14 Sun Cruising the South China Sea
15 Mon Singapore Arrive 8:00 am
16 Tue Singapore Depart 6:00 pm
17 Wed Cruising the Strait of Malacca
18 Thu Phuket, Thailand 8:00 am - 6:00 pm
19 Fri Cruising the Indian Ocean
20 Sat Cruising the Indian Ocean
21 Sun Colombo, Sri Lanka 8:00 am - 8:00 pm
22 Mon Cruising the Indian Ocean
23 Tue Mumbai (Bombay), India Arrive 1:00 pm
24 Wed Mumbai (Bombay), India Depart 11:59 pm
25 Thu Cruising the Arabian Sea
26 Fri Cruising the Arabian Sea
27 Sat Cruising the Arabian Sea
28 Sun Victoria, Seychelles 8:00 am - 6:00 pm
29 Mon Cruising the Indian Ocean
30 Tue Cruising the Indian Ocean
31 Wed Port Louis, Mauritius 8:00 am - 5:00 pm
April 2004
1 Thu Cruising the Indian Ocean
2 Fri Durban, South Africa Arrive 7:00 am
3 Sat Durban, South Africa Depart 6:00 pm
4 Sun Cruising the Indian Ocean
5 Mon Cape Town, South Africa Arrive 8:00 am
6 Tue Cape Town, South Africa Depart 5:00 pm
7 Wed Cruising the Atlantic Ocean
8 Thu Walvis Bay, Namibia 8:00 am - 6:00 pm
9 Fri Cruising the Atlantic Ocean
10 Sat Cruising the Atlantic Ocean
11 Sun Cruising the Atlantic Ocean
12 Mon Cruising the Atlantic Ocean
13 Tue Cruising the Atlantic Ocean
14 Wed Cruising the Atlantic Ocean
15 Thu Las Palmas de Gran Canaria, Canary Islands 8:00 am - 10:00 pm
16 Fri Cruising the Atlantic Ocean
17 Sat Lisbon, Portugal 7:30 am - 5:00 pm
18 Sun Cruising the Atlantic Ocean
19 Mon Southampton, England Arrive 7:00 am