Personally, I wouldn't try it. Both are large and take time. Some people don't realize they are not near each other. It's 30 miles outside San Diego to get to the safari park but you have to consider the traffic getting into and out of San Diego. We made the mistake of coming back into San Diego during rush hour - awful! We just left when the park closed and didn't think too much about how bad it could be.
The winter hours for your dates are:
Zoo: 9am - 8pm
Safari park: 9am - 6pm
Maybe someone with experience in the area might know how to manage both in one day. But I really think you will be pushing to get both done and may not enjoy either park if you feel rushed, especially with a little one. They both need a full day. Especially if you've never been (and even if you have).
I would personally really recommend the zoo. It is top notch, really beautiful and great enclosures for the animals. A large zoo with a LOT of variety of animals. Also, if you did happen to end early, Balboa Park is right there - the zoo is actually considered part of it.
There are activities for families with children too:
http://www.balboapark.org/visit/kids
If you go to the zoo with a little one, I would recommend paying the extra to take their tram around. You can get on and off at points. I remember the hike up to the polar bears was a HIKE.
The zoo website has an activity page for children:
http://kids.sandiegozoo.org/
There are also special experiences you can pay extra for to get up close with some of the animals.
http://www.sandiegozoo.org/zoo/index.php
There are only three zoos in the US with pandas. San Diego (has three), Atlanta and Memphis. (The Smithsonian in D.C. was suppose to give back their panda in 2010.)
I would happily go back repeatedly to the zoo. If I was told I couldn't go back to the safari park it wouldn't bother me.
This map may give you an idea of the scope of the zoo:
http://www.sandiegozoo.org/zoo/zoo_map
If you download the pdf file of the map and enlarge it you will see on the far left down low there is a petting zoo and a Fisher-Price discovery playground for little ones. There are several "theaters" with live shows during the day.