Should "look at her" be "looked at her"?

"Look at her" is right. Such constructions use the present tense for the avoided action.

I left the restaurant rather than eat the fish.
He covered his eyes rather than look at the dead man.

What an interesting construction.
Would any one like to talk more about it?

It's too common to be interesting.

Correction:

In this format (verb) rather than (verb) it is actually the 'base form' or bare infinitive of the second verb that is used.

I kept quiet rather than argue with my father.
I am walking to work rather than use the bus.
We will send emails rather than write letters.

Note that parallelism is recommended in such formats as this

I am driving rather than walking to work because I am late.
You should walk rather than run to the nearest exit if the fire alarm sounds.

I offer this extract, without comment, from the American Heritage Book of English Usage

The phrase rather than consists of an adverb and a conjunction and often means “and not,” as in I decided to skip lunch rather than eat in the cafeteria again. It is grammatically similar to sooner than in that it is used with a “bare” infinitive—an infinitive minus to: I would stay here and eat flies sooner than go with them.

Rather than can also be used with nouns as a compound preposition meaning “instead of”: I bought a mountain bike rather than a ten-speed. But some people object to this use, insisting that than should be used only as a conjunction. They therefore object to constructions in which rather than is followed by a gerund, as in Rather than buying a new car, I kept my old one. [Editor's note: these people are clearly insane. rather than + gerund is just fine, as is rather than + noun phrase.]

In some cases, however, rather than can only be followed by a gerund and not by a bare infinitive. If the main verb of the sentence has a form that does not allow parallel treatment of the verb following rather than, you cannot use a bare infinitive, and you must use a gerund. This is often the case when the main verb is in a past tense or has a participle. Thus, you must say The results of the study, rather than ending (not end or ended) the controversy, only added to it. If the main verb was in the present tense (add), you could use the bare infinitive end.

Curiously, when the rather than construction follows the main verb, it can use other verb forms besides the bare infinitive. Thus you can say The results of the study added to the controversy rather than ended it.

The overriding concern in all of this should be to avoid faulty parallels, as in sentences like Rather than buy a new car, I have kept my old one and Rather than take a cab, she is going on foot.

Thank you Contrex.
It seems quite subtle. To grasp the correct usage in different environments is not an easy task.
I have a few questions about it. But my stomach is in mild pain. I will post later.
Good day to you all.