How long it takes to appeal for a denied H1b visa with the USCIS?

There is not a specific time. Your lawyer, of course, is the best person to ask. Put the question to her. Good luck.

Appeals can take 12-18 months. In the meantime you are not in lawful status. You should consider your alternatives. I would seriously explore the possibility of filing another I-129 with another petitioner for consular pick up instead of an in-country extension/change of status. You need to avoid accrual of 180 days of unlawful presence before departure. The sooner you depart the US, the more sympathetic the consular officer will be in your home country on the application on the new approved visa. Fee free to call us to schedule your free initial consultation to give you a better idea of the options available to you and the time limits for those options.