A friend and I ran a new circuit from the panel (15A breaker) for a
switched vanity light and GFCI outlet in the bathroom. I am planning to
connect an exhaust fan/light (not over tub) taking power from the new
circuit via the vanity light switch and connecting to a dual switch
(top - fan, bottom - light) the light and fan will be independent of
each other.

I have the following:
working:
main switch/vanity light: hot (black) feed to switch H1, hot (black)
feed to light from switch H2, grounds connected and terminated on
switch G1, neutrals connected.

in progress:
fan: separate line (blue to black - hot, white to white - neutral)
ground on fan housing, leads in switch box ready for dual switch
connection.
light: separate line (black to black - hot, white to white - neutral)
ground on fan housing, leads in switch box ready for dual switch
connection.

My question is how do I complete the wiring for the dual switch (fan
and ligh)t? I would like to use the common hot and keep the tab (on
switch) in place to save room in the switch box.

My guess is that I can jump the hot lead from main switch to the dual
switch, jump the neutrals to the dual switch and connect the common
grounds. Something tells me that this is too simple based on the wiring
for the main switch/vanity light. Any feedback is greatly appreciated.