I read some of your other messages and liked your idea of making putting into the car seat a game. That sort of creativity is what will get you through the years with your baby.
You say that your baby has been independent up until now. She wasn't independent. She just had needs that were easy to meet. She ate and slept most of the time. Now she is beginning to develop a personality and she needs you to interact with her. This need is more difficult to meet but it's every bit as important as food and sleep.
You do need to find ways to have time for yourself but if you do that at the expense of not being with your daughter she will not develop in a healthy way and you will have even more difficulty getting mommy time as she grows older and demands your attention in negative ways.
I found that I eventually gained relief from the constant responsibility of taking care of my daughter by the time she was old enough to play at someone elses house. I had good friends whom I trusted and this started around age 7 or so.
Now, you could hire a babysitter and/or have friends or relatives watch her some of the time but there is no way that you are going to make her independent and able to play by herself. She will eventually learn to play by herself for short periods of time several months from now but she will only be able to do that if you teach her how to play and spend more time with her now.
I know it's difficult having a little baby totally dependent on you. And you do need mommy time. It's just that you can't do it by expecting a 4 month old baby take care of itself.
The ideas about a swing and toys with lights and action are helpful for short periods of time but I didn't feel that I really had time for myself during those times because I still had to keep an eye on her. My mommy time came when she was asleep or with a babysitter or friend.