My boat had a shower with a fairly deep tray. No idea if yours is the same? I fitted a plug and made a sort of splash pool for her to have a bath in. But for a really little baby, I'd probably just spread a towel on the floor and use a washing up bowl.
If you need a shower, just shower! A baby is unlikely to fall off the boat, esp if the doors are shut. I don't know your boat layout, but for a very young baby, I'd put her on the bed and stop any rolling by building a raised wall by stuffing a few rolled towels or cushions under the duvet. If older, a bouncy chair in the doorway of the bathroom so she can see you (the really cheap type that folds flat and can fit under a bed)?
Baby can sleep in a carrycot for a while. Then.... again it depends on your boat layout. Mine was two berth so DD had her own tiny cabin. If you have a master cabin and room for a pull-out bed in the living space, I'd probably have given DD the proper bed, just because having a bed permanently out for naps and early nights is a good thing. You can then use the living space unhindered, well past baby bedtime, and pull out your own bed when you feel tired yourself.
I'd recommend getting to know good places to go if the weather is awful. Somewhere your child can stretch its legs and run around. Also, use the showers at the local swimming pool as a good opportunity to have a damn good wash!
Feel free to message me if you like.