may Allah accept your umrah

u can wear ihram from ur home in doha itself... it may notbe convienient to wear it on plane or at airport
makkah is some 65 km from jeddah airport. it will take around 90 minutes from airport to makkah.
if u can speak arabic, then it will not be a proble,. there are taxi operators who will take u to makkah.

concentrate on ur ibadat. u can do shopping else where.
i hope u know umrah steps or u can get a book in doha and read about it.
u have a lot of restaurants, grocery stores and food chains. u will not have problem with food there.

while returning back from makkah to jeddah airport, plan to be atleast 4-5 hours in airport before ur plane departs.