H4 to H1 transfer: Need to stay for some months?

[aru123n]

Hi. I recently got an H4 Visa, and I plan to travel to the US for the first time in mid July 2012. I wish to convert my H4 to H1B if I find an employer.

Is there any law which requires me to stay in the US on H4 for a specified number of months before I can apply for H1B? If yes, then how long is this period?

[kabkaba]

There is no such requirement.
However, the annual cap for H1B may not remain open until July. If open, the earliest start date is Oct 1. Also, you cannot begin working until change of status to H1 gets approved. After change of status is approved you must begin working.