“Are you planning on asking her out?”
Your friend seems to be attracted to his co-worker. You want to find out what he's going to do about it. You ask this.
Are you planning on asking her out?
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(someone) is planning on (doing something)
When you are "planning on" doing something, it means that you intend to do it. You want to do it. But it doesn't necessarily mean that you have a strong plan for getting it done. For example, you can say:
I'm planning on throwing a big party for Kevin's 30th birthday in November.
If you say this in May, it doesn't mean that you've planned out a party. It just means that you think you're going to do it.
ask (someone) out
To "ask someone out" means to invite them to go on a date with you.