help! intro to 4week adopted kitten to my 8 month cat

Hi i hope you might be able to take a minute to give me some advice plz. About 2 months ago a 6 month old stray addopted us.we Took her to vet for her checked out. Shots.. and fixed.about 2 weeks ago my mom found a litter of 3 stray kittens .. newborns. Mother abandoned them. Ive keept one. Shes now 4 weeks. At first i keept her behind doors for a week so my older cat can smell her. Ive since opened door. My older cat ran up close to her and growled.so i went and bought a baby gate. She stares at the kitten. I feed them at same time.. one on each side so they can see eachother eat. I leave a small space at bottom so they can touch and play each others paws. That happened once. Older cat sits in front of the baby gate and when the kitten walks up close my older one growls. But doesnt growl when they eat. I treat my older one the same as i Did before... Maby give her a lil extra attention to let her know i love her. Am i doing everything right? When do i take the gate away? Keep in mind the kitten is 4 weeks.I don't want her to get hurt. She's very playfull and is fine around my dog.help!

Welcome to the forums @joie

Here are some tip to help with introductions

http://www.thecatsite.com/a/introdu...www.thecatsite.com/a/introducing-cats-to-cats

http://www.catbehaviorassociates.com/a-simple-little-trick-to-use-during-new-cat-introductions/

http://www.aspca.org/pet-care/virtual-pet-behaviorist/cat-behavior/introducing-your-cat-new-cat

http://jacksongalaxy.com/2010/10/01/cat-to-cat-introductions/

And a video to help too