I have done that trip in the reverse direction but you need to consider the winds in your direction. I would leave Galveston in April and
head for
Key West (assuming that your
mast won't clear the 48' Okeechobie bridge). Winds for that leg should be from the northeast mostly. If you catch a strong cold front then you can ride a north
wind most of the way, but it will be cold
Then
work your way up the keys and wait for the fronts to pass and the winds to shift east before making the trip up the
east coast. If necessary you can go inside the
ICW if you can't make progress against a north
wind.
You can do it as late as June, but after that hurricanes will be too much of a risk. Later in the year you could leave in late October after the hurricanes fade out, but it will be cold heading up the
east coast.
David