My understanding is that the general "rule" is that you can't start IVF until 3 months after weaning. The reason being that the hormones related to BF (eg elevated prolactin) can actually reduce the chance of the IVF working. That said, the actual policy will vary from one Dr to the next, so your best bet is to contact your FS and ask what their policy is. I have heard of some allowing women to cycle earlier, but I know others simply won't. You just have to ask.

Given your circumstances, I would hope your GP could give you a referral immediately. Like you, I wouldn't want to wait any longer than necessary. The fact that you only got 3 eggs suggests to me that you're a poor responder (or was it by design?), in which case, you may be in the same boat as me with DOR, meaning that clock is ticking even louder...