Singleton axe can make this very bad. Luckily since Cathy already has BW you can keep talking [now and further on] with her until she says that her best units is. In case of axe don't do that.
Holkan rush is doable overall, partially due to thei inner immunity to first strikes which helps against archers a bit. Rax is must in such case CRI holkans make cut but you need arround 3 per fortified archer to avoid problems.
You still need to attack with brains, for example at moment she sends settler with some archers out, attacking cap first and using fastest approach available.
Another problem is hse knows some other AI, as she spills espionage on you and AI x.
This is a problem since you do not know who that is. If than is Mansa than fine, but believe me you do not want to rush her just to found you are tet-a-tet on continent with someone like Tokugawa...
2) Rex Peacefully and take her out with Phants + Cats
You do not have land to rex honestly. 5cities before construction is not REX, but that term is used same way as CE, SE... [stupidly that is].
IMO, your second warrior [nearly built], should explore west and tundra... that wheat spot might be not so bad if there is deer or crabs in same cross.
3) Research AH and look for horses after which Chariot or HA rush
IMo, holkans are better than chariots if she does not have copper.
Overall you have nice land for a three-four city empire, being financial with a bit juggling between cottages and mines you can prepare nice classical war - cats+something to kill her.
In days i played monarch i usually played as three/four city empire until maces and than killed someone cats+maces while teching to trebs, trebs+maces for another and so on... Given difficulty level i see no reason to rush Catty, unless you desperately want that marble for shiny wonders...
About chopping - i am lazy to search but few times i've read heavy chopping vs improvements+ grow equalizes arround turn 40-50 expansion wise. Except for fact that improvements first has ton of forest left to chop wonders or army....
Summarizing - block some land [preferably settling with food in first ring to avoid problems], found othe rneighbours and than probably start working towards construction...