I think what I would do in that situation is setup a pre-filed flight plan and then call Houston Hobby Tower is what I believe is the correct procedure and say "Hobby Tower, Cessna 8237T at Pearland pre-filed to Cherokee County Airport, Juliet, Sierra Oscar at 7,500 with information Papa. They'll give you a read back and let you know which airspace to stay out of and possibly give altitude restrictions and what not and let you know that you have a specific departure time frame to be airborne before the departure is considered cancelled and you have to call again. At least this is what we always did departing out of a class Golf airport heading into a class Charlie airport for landing... Most of the time we wouldn't even do that. We would just call tower after leaving the runway and let tower know we had a pre-filed flight plan on the books to so and so and had requested flight following and if able they would set us up from there. It's hard to tell in that nightmare of a sectional with all that crazy business going on but it looks like Bravo doesn't start over Pearland until 2,000ft, but remember that's AGL. So in your case your safe to take off and call as long as you stay clear of Bravo