Being a man, it's not my place to say what you should or shouldn't do, or how you will feel
, but when I got my plot, my wife was 6 months pregnant. There was no way she could have helped manage the plot before or once our son was born, both physically and mentally. Initially she could hardly walk for a few weeks, (big baby! ahem!), and then the lack of proper sleep meant she had little motivation to do anything major. After about a year she happily helped come and do some raking and hoeing with the baby in a carrier/sling and this was fine, but she couldn't bend down. At one point I put a small plastic sand pit in the allotment which kept my son busy whilst I'd do stuff, but if the weather was too cold/too hot/too wet, then it was difficult to stay on site for very long with him.
I'm not saying it's impossible to do and you may find it works out great. I can't tell if this is your first child, but from mine and my wife's experiences our thoughts on what parenting would be like to the reality were very different. People say it's a shock, but you dont believe it until it happens!! It may seem like a lovely experience digging the plot whilst your child chills for a few hours playing with the snails, but after a few minutes of them sitting in dirt, eating the soil, wondering off down the roads, the novelty wears thin!!
However, on a positive note, our children love our allotment. Once my son got a bit older he would come and help water and then pick the soft fruit, look for spuds, pick courgettes etc. My second child is now 3 and she has helped plant all my veg this year and all the seeds. They get so much out of it and they've learnt loads and have no weird eating habits. All veg is eaten as they've seen it growing, helped to nurture it and pick it, so it's exciting! My son's favorite food is sprouts and he even asked for them for his special birthday dinner!! I couldn't get rid of my plot as the kids get so much out of it and that brings enjoyment to us.
If you do take it on, I'd suggest covering it in weed plastic to make it as maintenance free as possible. Grow stuff through that and just start small. Do a bit here and there and look at the long term goal rather than the trying to do everything at once and being overwhelmed. I've had my plot 6 years and it's only been this year that I've managed to get it to the point that I'm pretty happy with it.
Good luck!!