The sentence appears in an English textbook. The reason why it sounds off to me is that the first sentence is in the present simple tense. I expect it to be in the present continuous tense, like this:
We’re planning to go to the forest. Do you want to come?
The reason I say that is that if for example we added an adverb of frequency to the first sentence, it wouldn’t make sense in that dialogue.
We usually/always/often plan to go to the forest. Do you want to come?
It doesn’t make sense, because they’re planning to go to the forest now. It’s not something they do on a regular basis or even rarely. The whole thing is about this one single instance of going to the forest.
There is no error. The "stative" sense of plan, which allows it to be used like this is part of its meaning. So you can consider this construction to be idiomatically correct.
Another stative verb, with which you may be familiar, is "live". And just as both "I live in …" and "I’m living in …" are correct, so both "We plan" and "We’re planning" are correct.
The difference is that "We’re planning" could mean "Right now we are making our plan". Whereas "We plan" means "We have made a plan". But in many contexts both are possible. In the example you give, both are possible.