Your race scares me.
Great! The Killocats rely on psychological intimidation! Good to see that it works. ;-)

Good idea, I like it, but through my eyes its going to be a monster race.If any other race went one a one on one with the Killocats, I bet your race would wipe space clean with them and then some.
To be more serious, I am actually not overly concerned about the relative strength of the individual races, because Tim Wisseman (and most likely his group of betatesters) will balance the races against each other anyhow. With only limited knowledge how Version 4 will work and how the other races will defined and coded, it is impossible to fine tune a race at this point of time anyhow. Therefore my main aim at the moment is to reflect as many attributes of the original Kilrathi as possible in our race design.

Economic strength is stable
As I understand it, most of the money in V4 is generated in cities. Since Killocats have problems to live too closely to each other in cities, their economic power should be affected significantly.

starship strength is going to great
Is it? They got good carries (because the original Kilrathi do have "Super-Carriers",) but the carriers are not overly big and have only very few large and small weapons. So they will be quite vulnerable at close range. And if you compare their torpedo/missile based ships (the non-carriers), you will see that none of them is match for the larger Fed ships (and the Feds do not have the best torpedo-ships!). Ships in V4 can have up to 20 large and 30 small weapons: none of the Killocats ships has even half of that (the Leopard, as the ship with the most weapons, has 8 large and 15 small weapons).

ground combat strength,
Yes, this is another original Kilrathi attribute. However good ground assault values can be used as offensive weapon only if you have cloakers. Since the Killocats have none, their ground fighting abilities can be used in most cases only defensively. And transporting clans with cloaked fighters will be very inefficient and costly compared to cloaking ships.

you grow like rabbits,
This should actually be more of a disadvantage than an advantage. We have to see during beta-testing how well players will be able to handle an elevated growth rate.

your fighters rip through mine fields, cloak, and other neat things,
Yes, fighters are THE specialty of the Killocats. However the Killocat fighters are very expensive. They are even more expensive than the fighters of the Feds, which as a non-fighter race should have a very unfavorable relationship between fighter performance and price. We have to wait until we know at what prices the fighter-races will have access to what kind of fighter performance to balance the Killocat fighters.

plus they can be built in space.
Which will be more expensive than building them on the ground. The ability to be able to build fighters on some ships could be removed, but whether this is advisable depends very much on how the other races will get their fighters.

The only weakness I can see is the spy level, and a unstable happiness level.
Which should cause an unstable economy too.
Other disadvantages:
No cloakers
No hyperjumpers (which are likely to be much more important in V4!)
No good ships for close combat
No other good special abilities apart from the fighters
Most ships are specialized and good for only one task, so fleets of several ship designs must be built and operated together (lack of good all-purpose ships).

Maybe you could put some economic restrictions on them for their type of government,
we might reduce the income per city or limit the number of cities on a planet, if betatesting shows too much economic strength

or raise the price of fighters.
See above. Without knowing how the other races will get fighters, this is just speculation.

What about lower the climate bandwidth.
This sounds like a very good idea: giving them a narrow climate range where they grow extremely well (and where overpopulation problems have constantly to be managed) and a wide climate range where they grow only very slowly (if at all) and cannot build farms.

How about alliance, you can not have a full alliance with any race.
Are you referring to native races or player controlled races? I still do not understand well enough how the native races in V4 will work to answer the first option and the second option does not seem viable. If two players decide that they want to be fully allied, who or what is going to stop them?