This is a job that you want and could secure your income stream in the near future, keep your career going long term and have a big impact on your future earning potential. Do not bear this burden alone, share it with your husband.
There are women who go back to work after a very short time off when they have a baby. They do this with support. Could you get a nanny with experience of care of a newborn, a post natal doula or some other form of at home care for the first few months? It could be done with regular housekeeping and food preparation support, but it is likely that having someone who can hold your baby while you work will also be required. Yes, in the first month, breastfed babies can feed 8 to 12 times a day for 45 minutes at a time.. this can mean you could be feeding 50% of the time. (That is one end of the spectrum). After a month, there will be guaranteed longer gaps.
You have a husband. The financial impact and logistical adaptation required resulting from your pregnancy and the care of your baby should be shared between you and your husband.
Does your husband's place of work offer flexible working, work life balance, shared parental leave or any other options for him to take a role in taking care of your child so that you can do the 15 to 18 hours work required? If he could share the paternal leave, then he could have up to 50 weeks of leave and 37 weeks of pay. If he could request parental leave (unpaid leave in blocks of 2 weeks, giving the required notice etc) and use this to help. He could also arrange to have one or two days holiday per week which would get you through around 3 months where he can support you through those days to carve out enough time to work - if you really can get your content done without needing to be totally focussed.
Yes, family time together at weekends would be nice, but there are 24 hours in the day and 7 days a week.. your husband has to work for 40, you have to work for 15 and your baby needs care for 168 of those hours, though they will likely sleep for large portions of that, however there is no guarantee that they will sleep without company. You can prioritise your work and have some family time together without insisting that you stick to father goes to work Monday to Friday, Mother has baby clean and happy, food on the table when he gets home and pretends all of her needs are met and weekends are some blissful time where you look lovingly at each other and your baby and nothing else gets done. Real life is not like that... housework, baby, contracting work all needs to get done as and when it fits... I work part time, flexibly, this often happens when my husband is home. We still make time for each other but I also make sure there is time carved out for my work. My kids are older and I did not work when they were babies.. but people do... find them and find out how it works for them! Get help and do not compare the cost of help with the income you earn. By being at home, you are facilitating your husband's income too.
You could let your prospective collaborator know that you have a prior commitment during the month of June where you would not be available for work for 4 weeks when they offer the job. The challenge will be that your baby could arrive 2 weeks early or 2 weeks late. However, depending on how they react to that knowledge and the fact that you will have 3 months to make a good impression on them, they might be able to be flexible in their demands and requests around that time. You might also be able to get someone to help you meet their requirements.
There are many ways to solve this situation... keep brainstorming!! Maybe ask this in the freelancing section too..