A refused EE app will not affect a sponsorship app and vice versa.After speaking with my partner about this again, we are worried that if I go for EE and I'm refused then that jeopardizes applying for sponsorship.
Can we apply for sponsorship now, and then apply for EE in 4 months when I've worked at my job for a year?
You can apply for both but you will be required to pay the fees for both. Depending on where you are in each process when you get an approval on one, you may not get a refund from the other. Also note that EE requires you pay for language testing and having your foreign education assessed. Sponsorship doesn't require any of that.
You should look at the London thread in the Family Class section of the forum, as there is a good spreadsheet of timelines. Last time I looked, London averaged about 8 months.