NO. It's not copyright infringement. It does, however, appear to be cybersquatting, trademark infringement, servicemark infringement, fraud, trademark dilution and unfair competition if you try to sell it. You are seriously illegal and need to get an attorney's advice. You should abandon the domain to mitigate your damages before before FOX gets wind of this and tracks you down. What a dumb stunt!
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
By itself, a domain name registration is unlikely to result in a claim of copyright infringement. However, it may give rise to the claim of cybersquatting, regardless of whether you try to sell it or not. Cybersquatting under the ACPA requires a showing that the offending domain name was registered or trafficked or used in bad faith. Registering a domain name simply to park it rather than use it could be considered bad faith, but using the domain name for a website that comments on the Family Guy TV show could be considered a good-faith use. It depends on the specific facts. In addition to cybersquatting suit under federal law, there may also be unfair competition violations under state law, or an arbitration to have ICANN transfer the domain name in a UDRP action filed with WIPO. You need to consult with a trademark attorney if you are concerned about your domain name registration.
This answer is for informational purposes only. It is not intended as specific legal advice regarding your question. The answer could be different if all of the facts were known. This answer does not establish an attorney-client relationship.
Your purchase of this infringing domain name constitutes a violation of the Anticybersquatting Consumer Protection Act, § 43(d) of the Lanham Act. This domain names appears on its face to be confusingly similar to the FOX mark and the Family Guy mark, to create a false association with the same, and to have been registered as a domain name long after those marks became famous and distinctive. Assuming as much, your purchase and use of this domain would therefore constitute trademark infringement, willful false designation of origin and unfair competition under the Lanham Act, 15 U.S.C §§1114 and 1125(a), entitling FOX to (1) injunctive relief pursuant to 15 U.S.C §1116, Section 34 of Lanham Act; and (2) monetary relief pursuant to 15 U.S.C §1117, Section 35 of the Lanham Act equal to three times the amount of your profits or their damages, whichever is greater, plus their reasonable attorney’s fees. You need to consult counsel and obtain advice.
The information that is placed in this response is for informational purposes only and does not create an attorney-client relationship with Thomas P. Howard, Esq., nor is it intended to be relied upon as a replacement for legal advice from an attorney.